Complete the proof of the identity by choosing the Rule that justifies each step.
(1- cos x) so
secx sin tan
To see a detailed description of a Rule, select the More Information Button to the right of the Rule,
Answers
( 1 - cos²x ) secx
=> sin²x . secx
Here the rule ( rule 1 ) is the first trigonometric identity [ sin²A + cos²A = 1 ] by simplifying we have , [ 1 - cos²A = sin² ] . So here we substituted 1 - cos²x = sin²x .
=> sin²x [ 1/cosx ]
Here the rule ( rule 2 ) is secx = 1/cosx . So here we substituted secx = 1/cosx .
=> sinx [ sinx/cosx ]
Here the rule ( rule 3 ) is sin²x can be written as sinx . sinx , so we get sinx . sinx [ 1/cosx ] next by simplifying , sinx [ sinx/cosx ].
=> sinx tanx
Here the rule ( rule 4 ) is , in the above we got sinx/cosx and here we know that , sinx/cosx = tanx . So we have tan x .
The proof of the identity that justifies that ( 1 - cos²x ) secx equals sinx(tanx) has been described below with statements and rules.
Statement 1; ( 1 - cos²x ) secx
This is given
Statement 2; sin²x · secx
Rule 1; From trigonometric identities, we know that;
sin²x + cos²x = 1,
Thus; cos²x = 1 - sin²x
Thus; ( 1 - cos²x ) secx = sin²x · secx
Statement 3; sin²x (1/cosx)
Rule 2; The rule here according to trigionometric identities is that; secx = 1/cosx. Thus; secx = 1/cosx .
Statement 4; sinx (sinx/cosx )
Rule 3; The rule here is that sin²x can be expressed as (sinx * sinx)
Thus, we have; sinx . sinx (1/cosx) = sinx (sinx/cosx ).
Statement 5; sinx(tanx)
Rule 4; The rule here is that; sinx/cosx = tanx.
Thus; sinx (sinx/cosx ) gives us sinx(tanx)
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Related Questions
Find the factor of 30
Answers
Step-by-step explanation:
The factors of number 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
hope it helps!
Answer:
the factors of 30 are 1, 2, 3, 5, 6, 10
Step-by-step explanation:
hope this helps
please mark me as brainliest
Please help me I’m desperate
Answers
Answer:
7/10:3/5=7/10×5/3=35/30=7/6
Answer:
5. 7/10 × 5/3
6. 3/5 ÷ 7/10
Step-by-step explanation:
5. 7/10 ÷ 3/5 = 7/10 × 5/3
6. 3/5 ÷ 7/10
15r-15s=
can you help
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Answer:
=15r−15s
or if it is a factor:
15(r−s)
I don’t know how to do this
Answers
Answer:
Step-by-step explanation:
The first box should be 20.
The second box should be 40
The third box should be .2
The fourth box should be .6
Rashawn knows the multiplications 6x4 and 2x4. How can he use their products to find 8x4?
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Answer:
Since 6x4=24
and
2x4=8,
we can tell that these answers are common multiples of 8, and so 24 plus 8 equals 32.
Step-by-step explanation:
8x4=32
Graph the equation by plotting three points. If all three are correct, the line will appear. 2y = 5x + 11
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Answer: (-1,3) (-2, 0.5) (0,5.5)
Step-by-step explanation:
Please help thank u I appreciate it
Answers
9514 1404 393
Answer:
m∠ADC = 86°
Step-by-step explanation:
The sum of angles making a straight angle is 180°, so we have ...
(6x +52)° +(9x +23)° = 180°
15x = 105 . . . . . subtract 75°, collect terms, divide by °
x = 7 . . . . . . . . . divide by 15
m∠ADC = (9·7 +23)°
m∠ADC = 86°
Here given that ,
Line BDA is a straight line Angles on the line BDA are ∠BDC & ∠ADCAs we know that , sum of angles on a straight line is always equal to 180° . So ,
=> ( 6x + 52 ) ° + ( 9x + 23 ) ° = 180°
=> 15x + 75° = 180°
=> 15x = 180° - 75°
=> 15x = 105°
=> x = 105°/15
=> x = 7°
Now , by the given information , we need to find the value of ∠ADC
∠ADC = ( 9x + 23 ) °Now substituting the value of x ,
⇒ ∠ADC = 9x + 23
⇒ ∠ADC = 9 ( 7 ) + 23
⇒ ∠ADC = 63 + 23
⇒ ∠ADC = 86°
find the gretest number which devded by 181 and 236 leave a remainder of 5 in each case
Answers
Answer:
The greatest number is 11
Step-by-step explanation:
Given
Dividends: 181 and 236
Remainder: 5
Required
Determine a divisor that satisfies the above condition
Let the required divisor be represented with x.
Since a remainder of 5 is expected, then x can divide (181 - 5) and (236 - 5) without remainders.
So, we have:
[tex]181 - 5 = 176[/tex]
[tex]236 - 5 = 231[/tex]
Next, we calculate the GCF of 176 and 231
[tex]176 = 2 * 2 * 2 * 2 * 11[/tex]
[tex]231 = 3 * 7 * 11[/tex]
The greatest common factor, GCT is:
[tex]GCF = 11[/tex]
Hence, the required divisor is 11
which number is an integers
-3/4
1/5
2
42/3
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Millions of students take statistics each year! Researchers hoping to help professors teach better conducted a study in statistics classrooms. They had the same instructor teach three different classes, with randomly assigned students, with three different methods! Method A - traditional lectures, with homework outside of class. Method B - flipped classroom, with students watching videos of lectures and working on homework in class with peers and instructor. Method C - fully online, with students watching videos of lectures, with homework outside of class. They then gave each class the same final exam (out of 20 points). These were the results:
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Answer:
It doesnt show the results
Step-by-step explanation:
Which model can be used to subtract 1/2 from 5/6?
Answers
Answer:
2nd one
Step-by-step explanation:
1/2 when multiplied with 3/3 so it has the same denominator is 3/6, the second choice shows 3/6 as a model as well as 5/6 so yea
What is the answer to 3- a/7=-2 ?
Answers
Step-by-step explanation:
3 - a/7 = -2
a/7 = 5
Therefore a = 35.
Translate this sentence into an equation.
108 is the product of Carlo's age and 6.
Answers
Answer:
Step-by-step explanation:
Let Carlo's age = x
Equation: 6*x = 108
6x = 108
Solution:
6x = 108
x = 108/6
x = 18
Carlo's age = 18 years
Answer:
Solution :-Let the age of Carlo be x
[tex] \tt \: equation \longrightarrow \: 6x = 108[/tex]
Age
[tex] \tt \: 6x= 108[/tex]
[tex] \tt \: x \: = \dfrac{108}{6 } = 18[/tex]
What is the missing length for this one???
Answers
Answer:
45√2
i am pretty sure this is it
Does anyone know the answers to the Geometry test? I need help with the answers on transformation and congruence
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Answer:
We can surely help you on your geometry test. Please post the questions and our experts will gladly help you!What is the answer for this math problem
Answers
Answer:
The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2) ⇒ D
Step-by-step explanation:
To solve this type of question, Form the equation of the line and substitute the x-coordinate of each ordered pair to find y, if the value of y equal to the value of the y-coordinate of the point, then the point is on the line
The form of the linear equation is y = m x + b, where
m is the slope of the lineb is the y-intercept (value y at x = 0The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]From the given figure
∵ The line passes through points (-4, 0) and (0, 4)
∴ x1 = -4 and y1 = 0
∴ x2 = 0 and y2 = 4
→ Substitute them in the rule above
∵ m = [tex]\frac{4-0}{0--4}[/tex] = [tex]\frac{4}{0+4}[/tex] = [tex]\frac{4}{4}[/tex]
∴ m = 1
∵ b is the value of y at x = 0
∵ y = 4 at x = 0
∴ b = 4
→ Substitute the values of m and b in the form of the equation above
∴ y = 1(x) + 4
∴ y = x + 4 ⇒ equation of the given line
Let us check every group
∵ The ordered pairs are (7, 3), (6, 2), (2, -2)
∵ y = x + 4
∵ x = 7
∵ y = 7 + 4 = 11
∵ y-coordinate = 3
∴ Point (7, 3) doesn't lie on the line
∵ The ordered pairs are (5, 1), (3, 7), (2, 6)
∵ x = 5
∴ y = 5 + 4 = 9
∵ y-coordinate = 1
∴ Point (5, 1) doesn't lie on the line
∵ The ordered pairs are (3, 7), (2, 6), (2, 2)
∵ x = 3
∴ y = 3 + 4 = 7
∵ y-coordinate = 7
∴ Point (3, 7) lies on the line
∵ x = 2
∴ y = 2 + 4 = 6
∵ y-coordinate = 6
∴ Point (2, 6) lies on the line
∵ x = 2
∴ y = 6
∵ y-coordinate = 2
∴ Point (2, 2) doesn't lie on the line
∵ The ordered pairs are (3, 7), (2, 6), (-2, 2)
∵ x = 3
∴ y = 3 + 4 = 7
∵ y-coordinate = 7
∴ Point (3, 7) lies on the line
∵ x = 2
∴ y = 2 + 4 = 6
∵ y-coordinate = 6
∴ Point (2, 6) lies on the line
∵ x = -2
∴ y = -2 + 4 = 2
∵ y-coordinate = 2
∴ Point (-2, 2) lies on the line
∵ The three ordered pairs lie on the line
∴ The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2)
∵ The ordered pairs are (1, 5), (-6, 2), (-7, -3)
∵ x = 1
∴ y = 1 + 4 = 5
∵ y-coordinate = 5
∴ Point (1, 5) lies on the line
∵ x = -6
∴ y = -6 + 4 = -2
∵ y-coordinate = 2
∴ Point (-6, 2) doesn't lie on the line
There are 6 2/3 pounds of walnuts in a container, which will be divided equally into containers that hold 1 1/2pounds. This would fill and 4/9 containers. (3 points)
Answers
Step-by-step explanation:
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Many ancient tombs were cut from limestone rock that contained uranium. Since most such tombs are not well-ventilated, they may contain radon gas. In one study, the radon levels in a sample of 12 tombs in a particular region were measured in becquerels per cubic meter (Bq/m3). For this data, assume that x(over-bar)= 3,469 Bq/m3 and s= 1,135 Bq/m3. Use this information to estimate, with 95% confidence, the mean level of radon exposure in tombs in the region. Interpret the resulting interval.
Answers
Answer:
95% confidence interval of the mean level of random exposure in tombs in the region.
(2746.868 , 4191.132)
Step-by-step explanation:
Step(i):-
Given sample size 'n'= 12
Mean of the sample x⁻ = 3,469
and standard deviation of the sample 's' = 1,135
95% confidence intervals are determined by
[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} +t_{0.05} \frac{S}{\sqrt{n} } )[/tex]
Degrees of freedom = n-1 = 12-1= 11
Step(ii):-
95% confidence intervals are determined by
[tex](3469- 2.201 \frac{1135}{\sqrt{12} } , 3469+2.201\frac{1135}{\sqrt{12} } )[/tex]
( 3469-722.132 , 3469 +722.132)
(2746.868 , 4191.132)
Explain how you found your answer
Answers
Answer:
let the total cost of a rug be x
then
30% of x =75
30/100*x =75
3x=750
x=750/3 = 250
Marc owe = 250-75 =175
Step-by-step explanation:
PLEASE HELP IT DUE RIGHT NOW!! PLEASE EXPLAIN THE STEPS TO THIS TOO!!
Answers
(-2-0)/(2+6) = -2/8 = -1/4
Y intercept: when x = 0
Y intercept: (0,-1.5)
Solution: the answer is H
Answer: y int = -1.5
Slope = -1/4
Step-by-step explanation: y int is the point at which the line cross the y axis.
Slope = rise/run
Starting from the point on the left of the graph (-6,0) and going the the other point (2, -2) you can see the it rises -2 point. (0 to -2) the it runs 8 point. (-6 to 2).
Therefore the Slope = -2/8 or -1/4
what is the area of a cube each side is 6 cm
Answers
Answer: 24.
Step-by-step explanation:
Answer:
A=126
hope that helps!!!!!!!!!!!
A pie crust recipe calls for 2 cups of butter for each 3 cups of flour. Ella is making enough
crusts to use 9 cups of flour. How many cups of butter will she need?
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Answer:
6 cups of butter because the ratio is 2/3 and if you keep with that you will get 6 cups ep-by-step explanation:
Given that a baby is 8month and her elder sister is 4 years old, express their ages as a ratio
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Answer:
the ratio: 6:1
Step-by-step explanation:
to make it as a ratio :
We will make 4 years as months
So 4x12 =48
then the ratio: 48:8
6:1
hope this helps
Order of Operations make it true
5 23 18 8 4 = 100
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Answer:
Step-by-step explanation:
5 x (23-18) x (8-4)=100
5 x (23-18) x (8-4)=100 is the Order of Operations which make it true
What is Number system?A number system is defined as a system of writing to express numbers.
We have to find the operations which make the value to be true.
The given numbers are 5, 23, 18, 8, and 4.
Let us use the operation addition, subtraction and addition.
Use the subtraction between twenty three and eight.
Use subtraction between eight and four.
5 x (23-18) x (8-4)=100
Hence, 5 x (23-18) x (8-4)=100 is the Order of Operations which make it true
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Find the sum. Enter your answer in the box below as a fraction, using the
slash mark (/) for the fraction bar.
2/13 + 4/13
Answers
Answer:
6/13
Step-by-step explanation:
please help me i need help bad
Answers
Answer:
Line segment A' B' has a length of 2 units, and line segment C' D' has a length of 4 units.
Step-by-step explanation:
All we need to do is count the units in between the line segments.
What is it
Simplify
5(6-3)+2
Answers
Answer:
Step-by-step explanation:
17
Any help please thank you I appreciate it
Answers
Answer:
114.8 degrees
Step-by-step explanation:
supplementary angles basically means angles equal to 180 degrees
Solve the proportion.
x+1/×-1 = 14/20
A: - 3/17
B: 10/7
C: 7/10
D: -17/3
Answers
14x+14=20x-20
-6x=-34
x=34/6=-17/3
D: -17/3
Answer:
D
Step-by-step explanation:
x+1/x-1=14/20
so 20(x+1)=14(x-1)
20x+20=14x-14
20x-14x= -14-20
6x=-34
so x=-17/3
Given the line below, state the slope of the PARALLEL line. y=-8x + 10 what is the answer need help.
Answers
Step-by-step explanation:
the answer to this education is -8