Prove that: (1 + cos A)^2 - (1 - cos A)^2/
sin^2 A=
4cosec A. cotA​

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

cosec x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex]

Consider the left side

[tex]\frac{(1+cosA)^2-(1-cosA)^2}{sin^2A}[/tex] ← expand and simplify numerator

= [tex]\frac{1+2cosA+cos^2A-(1-2cosA+cos^2A}{sin^2A}[/tex]

= [tex]\frac{1+2cosA+cos^2A-1+2cosA-cos^2A}{sin^2A}[/tex]

= [tex]\frac{4cosA}{sin^2A}[/tex]

= 4 × [tex]\frac{1}{sinA}[/tex] × [tex]\frac{cosA}{sinA}[/tex]

= 4cosecAcotA

= right side,  thus proven


Related Questions

Suppose f(x)=x.Find the graph of f(x)+4

Answers

Answer:

Step-by-step explanation: the slope would be 1 and the y intercept would be 4.

If g(x) = x2 – 4, then what is g(-4)?
0 -20
0 -8
O 12
O 20

Answers

Answer:

g(- 4) = 12

Step-by-step explanation:

To evaluate g(- 4), substitute x = - 4 into g(x), that is

g(- 4) = (- 4)² - 4 = 16 - 4 = 12

Urgent please hurry!!

Answers

Answer:

c

Step-by-step explanation:

Answer: It is C

Hoped it helped

Step-by-step explanation:

choose the statement that correctly compares the unit rates

Answers

The answer would be B, because Carl is running more (7miles per min) , and Darren is only (5 miles per min)

HELP PLZ!!!i cant figure this out and dont worry about what else im typin it wont let me continue without having 20 word typed so I’m just typin but can u help plz

Answers

Answer:

The length is 42 inches and the width is 14 inches

Step-by-step explanation:

You know the width is 1/3 of the length, and the length is basically the longer side of a rectangle. The width is y-4, so multiply using distributive property to get 3y-12.

You now know that the 2y+6 is equal to 3y-12, so you add 12 to both sides using additive property of addition to get 2y+18=3y.

Then you subtract 2y from both sides to get the unit value of y.

Y is equal to 18.

Then you can plug 18 into the y's to get

2(18)+6 which is 36+6 = 42

18-4   = 14

There you go.

The length is the longer side which is 42 inches and the width is 14 inches

Hope this helps!

need help with #20 asap appreciate it

Answers

Answer:

The other endpoint would be (-7, -4)

Step-by-step explanation:

-10 - 2x < 6 and 6x + 12 < -6

Answers

Answer:

Step-by-step explanation

What the question about solve or what?

I have 40 softballs i give 5 softballs to each player. How many players can i give softballs to so that i have at most 10 softballs left

Answers

Answer:

6

Step-by-step explanation:

5 to each players means you have 6 players and then you have 10 left for yourself

Answer:

You can hand out 5 softballs to 6 players.

Step-by-step explanation:

In order to solve this problem, you need to divide 30 balls to each player (In order to have 10 left.) 30 divided by 5 is 6, so you can only hand out 5 balls to 6 players in order to have 10 left out of 40.

what is the quadrant of 51, -1

Answers

That would be quadrant 2 or quadrant ||

4(x+3)=4x+12
Please help me

Answers

Answer: x = 3

Step-by-step explanation:

Sebastian scored a 94% on a test. Frankie answered 43 questions correctly out of 50 total questions. Who scored higher on the test?

Answers

Answer:

Sebastian did.

Step-by-step explanation:

seb = 94% or 47/50

while frankie = 43/50 or 86%

Also look at 50 if you want and you can see it divides evenly with 100. Basically each mistake you make is 2 percent lost.

Answer: Sebastian

Step-by-step explanation: Divide 43 by 50.

43/50=0.86

tests are graded by the decimal point so he got 86%

since 94% is more than 86% sebastian scored higher

thank you in advance

how do i solve or come up for things like this for example:
write an equation for the line that passes through (3,-6) and (8,9)

Answers

Answer:

rise/run 6/15 6/15 = 0.4

Step-by-step explanation:

Answer:

y=15/-5x+5 OR y=-3x+5

Step-by-step explanation:

any answer works. the 2nd one is just the simplified version of the first one

Mary is a scientists. Using a microscope, sh looks at a salt crystal

Answers

Answer:

good for mary

Step-by-step explanation:

Lol the comment above me.

So Mary looked into a microscope, what about it? Whats the question?

PLEASE HELP ANSWER THIS ASAP

Answers

Answer:

B

Step-by-step explanation:

Open circle: < or >

Arrows point outward

Points located at 5 and 18

Answer:

a

Step-by-step explanation:

What is the slope of a line perpendicular to the line whose equation is x-2y=12? Fully reduce your answer

Answers

Answer:

First, we need to solve the equation in the problem for y to put it in slope-intercept form so we can determine its slope:

2y−6x=4

2y−6x+6x=6x+4

2y−0=6x+4

2y=6x+4

2y2=6x+42

2y2=(6x2)+(42)

y=3x+2

The slope-intercept form of a linear equation is: y=mx+b

Where m is the slope and b is the y-intercept value.

Therefore the slope of this equation is m=3

A perpendicular line will have a slope (let's call this slope mp) that is the negative inverse of this line. Or, mp=−1m

Substituting gives:

mp=−13

Answer:

-2

Step-by-step explanation:

Solve 5x3 – 23x2 + 29x – 15 = 0.

Answers

Answer:

its b

Step-by-step explanation:

Answer:

{x = 3, x = 4/5 + i(3/5), x = 4/5 - i(3/5)}

So B

given that 5x - 8y = 29 find y when x = -1 give your answer as an improper fraction​

Answers

Answer with step-by-step explanation:

If x = -1, we can re-write the equation as -5 - 8y = 29.

Step 1: Simplify both sides of the equation.

-5 - 8y = 29

-5 + (-8y) = 29

-8y - 5 = 29

Step 2: Add 5 to both sides.

-8y - 5 + 5 = 29 + 5

-8y = 34

Step 3: Divide both sides by -8.

-8y/-8 = 34/-8

y = -17/4

Hope this helped! (brainliest please)

What is the reflection of -3,3 over the y axis

Answers

Answer:

3,-3 on x axis

Step-by-step explanation:

If a rectangle is (x+2) wide and (x-7) in length, the area of the rectangle is? ​

Answers

Answer: x² - 5x - 14

Step-by-step explanation: Start with the formula for the area of a rectangle.

Area = length x width

To multiply these two binomials, let's use the F.O.I.L. method.

The product of the first terms is x².

The product of the outer terms is -7x.

The product of the inner terms is 2x.

The product of the last terms is -14.

So we have x² - 7x + 2x - 14 which simplifies to x² - 5x - 14.

solve y=-2/5x+1/10 as a standard notation

Answers

Answer:

4

x

+

10

y

=

10

Explanation:

Standard linear form is

XXX

A

x

+

B

y

=

C

with

A

,

B

,

C

Z

and

A

0

Given

XXX

y

=

2

5

x

+

1

10

Multiply both sides by

10

XXX

10

y

=

4

x

+

1

Add

4

x

to both sides

XXX

4

x

+

10

y

=

1

Step-by-step explanation:

PLEASE HELP! I left to go eat and when I came back I forgot what I was doing.
The image shown is of two sets of parallel lines.
The m∠ 13 = 29x - 2 and the m∠ 9 = 27x + 6
What is the m∠ 12?

Answers

Answer:

x=4

m<12 = 66

Step-by-step explanation:

Answer:

x = 4

m∠12 = 66

m∠13 and m∠12 are linear pairs (supplementry angles)

Step-by-step explanation:

m∠9 ≈ m∠15 (Vertical angle)

m∠15 ≈ m∠13 (Corresponding angle)

m∠9 ≈ m∠13

29x - 2 = 27x + 6

2x - 2 = 6

2x = 8

x = 4

m∠13 = 29(4) - 2

m∠13 = 114

m∠13 + m∠12 = 180

180 - m∠13 = m∠12

180 - 114 = 66

m∠12 = 66

HELP!!!!!!!!!!! Please like fast please and thank you

Answers

Answer:

C

Step-by-step explanation:

39-7=32

40-7=33

41-7=34

42-7=35

C is the concrete one that has

Picture attached !!!

Answers

Answer:

D.

Step-by-step explanation:

Since they are both the same angle measures, they are congruent, and also corresponding since they are located on the same side and half of the different lines.

The number 45 is no
more than the difference of 2 times a number m and 3.

Answers

Answer:

            m ∈ <24, ∞)

Step-by-step explanation:

m      - given number

2m      - 2 times the number m

2m-3     - the difference of 2 times the number m and 3

the number 45 is no  more than the difference of 2 times a number m and 3

       45   ≤   2m - 3

     -2m     -2m

45 - 2m  ≤  -3

  -45          -45

    - 2m  ≤  -48

    ÷(-2)      ÷(-2)

      m  ≥  24

m ∈ <24, ∞)

The ratio of men to women at a basketball game was 4:3. If there were 80 men at the basketball game, how many women were at the game?

Answers

Answer:

60

Step-by-step explanation:

braniest please

Help 33-37 please will score as brainliest

Answers

Answer:

See below

Step-by-step explanation:

Quadratic function is in general form of:

y = ax^2 + bx + c

The function has a minimum if a > 0 and maximum if a < 0

The minimum or maximum point is a vertex of the graph

A vertex is the point x = -b/2a

When b = 0, the min or max point equals to value of c.

33. It has maximum of -134. It has minimum of 735. It has minimum at x = - 8/4 = -2

f(-2) = 2*(-2)^2 + 8(-2) + 7 = 8 - 16 + 7 = - 1

36. It has maximum at x = -18/2(-3)= 3

g(3) = -3*3^2 + 18*3 - 5 = -27 + 54 - 5 = 22

37.  It has minimum at x = - 6/(2*3/2) = - 2

f(-2) = 3/2*(-2)^2 + 6(-2) + 4 = - 6 - 12 + 4 = - 14

help please!!!!! big assignment grade

Answers

Answer:

A

Step-by-step explanation:

plz ive been stuck on this for an hour plzzz help?​

Answers

Answer:

X=-2

Step-by-step explanation:

!:'=/,)_"86"&8_)&485)&($8

The right answer is x > (-2). x it greater than or equal to (-2)
-

Haley can read 5/8 pages in 2/3 minutes how many pages can she read in one minute

Answers

Given parameters:

Number of pages Haley can read = [tex]\frac{5}{8}[/tex] pages

Time to read the pages = [tex]\frac{2}{3}[/tex] min

Unknown:

Number of pages that can be read in 1 min = ?

Solution:

To solve this problem let us find Haley's rate;

       Rate  = [tex]\frac{Number of pages Haley can read}{Time }[/tex]

 Input the parameters and find the rate;

     Rate  = [tex]\frac{5}{8} / \frac{2}{3}[/tex]

     Rate  = [tex]\frac{5}{8} x \frac{3}{2}[/tex]

      Rate = [tex]\frac{15}{16}[/tex] pages/min

Now that we know the rate;  

   In 1 min; number of pages Haley can read;

               Number of pages  = Rate x time

                Number of pages  = [tex]\frac{15}{16}[/tex]  x   1  = [tex]\frac{15}{16}[/tex][tex]\frac{15}{16}[/tex] pages

Haley can read pages [tex]\frac{15}{16}[/tex]  in 1 minute.

Annie reads 8 1/3 pages of a book in 10 minutes. What is her average reading rate in pages per minute?

Answers

The answer is about 0.83333
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