how do you simplify
[tex] \frac{ \sin(90 - \alpha ) \times \tan( - \alpha ) \times \cos( \alpha - 180) }{ \ \cos(100) \sin(135?) } [/tex]

Answers

Answer 1

Answer:

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{\sqrt{2} \times sin(2 \times \alpha) }{2 \times cos(100^{\circ}) }[/tex]

Explanation:

The given expression is presented as follows;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})}[/tex]

The sine, cosine, and tangent of the common angles are given as follows;

sin(A - B) = sin(A)·cos(B) - cos(A)·sin(B)

∴ sin(90° - α) = sin(90°)·cos(α) - cos(90°)·sin(α) = cos(α)

tan(-α) = -tan(α)

cos(A - B) = cos(A)·cos(B) + sin(A)·sin(B)

∴ cos(α - 180°) = cos(α)·cos(180°) + sin(α)·sin(180°) = -cos(α)

sin(135°) = sin(90° + 45°) = sin(90°)·cos(45°) + sin(45°)·cos(90°) = cos(45°) = √2/2

Therefore, we get;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times -cos( 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{cos( \alpha) \times -tan (\alpha) \times -cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}}[/tex]

[tex]\dfrac{cos( \alpha) \times -\dfrac{sin(\alpha)}{cos(\alpha)} \times -cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}} = \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}} = \dfrac{2}{\sqrt{2} } \times \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) }[/tex]

[tex]\dfrac{2}{\sqrt{2} } \times \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) } = \dfrac{sin(2 \times \alpha) }{\sqrt{2} \times cos(100^{\circ}) }[/tex]

Therefore;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{\sqrt{2} \times sin(2 \times \alpha) }{2 \times cos(100^{\circ}) }[/tex]


Related Questions

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Answer:

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Answer:

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Answers

Answer:

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Explanation:

Code:

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Answer:

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Explanation:

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Answers

Answer:

Part A

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Part B

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Answers

Answer:

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Explanation:

Mountain farming is done in hilly areas of the mountains. It is mainly family farming. The mountain farming is mainly done in the mountains where the paddy fields are scattered and the limited use of the usable lands are available.

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Answer:

Here is your answer

Explanation:

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2. use environmentally household products such as washing powder, household cleaning agents

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Answer:

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Answers

Answer:

Step 1 : Start

Step2 : Input first number, num1

Step3 : Input second number, num2

Step4 : product - - > num1 * num2 (product of num1 and num2)

Step5 : Input product, myanswer

Step6 : comparison - - - > correct or incorrect based on myanswer and product

Step6: print(comparison)

Step7: End

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Required :

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Expected output

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Step2 : Input first number, num1

Step3 : Input second number, num2

Step4 : product - - > num1 * num2 (product of num1 and num2)

Step5 : Input product, myanswer

Step6 : comparison - - - > correct or incorrect based on myanswer and product

Step6: print(comparison)

Step7: End

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Answer:

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Answer:

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Under "Security," select Signing in to G oo gle.

Choose Password. You might need to sign in again.

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Answers

Answer:

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Answers

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Answers

Answer:

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Answers

Answer:

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50 PRINT TRIANGLE

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Get input for radius, base and height

10 INPUT RADIUS, BASE, HEIGHT

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Print area of circle

40 PRINT CIRCLE

Print area of triangle

50 PRINT TRIANGLE

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>3

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[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

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Answers

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Answer:

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Explanation:

Answer:

Explanation:

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Answers

Answer:

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Answers

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Answer:

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Answers

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[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

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Answer:

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