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11th Business Maths Weekly Test - 4 ( Trigonometry)

MABS Institution

11th Business Maths Weekly Test - 4 ( Trigonometry)-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

Prove that\(\left\{1+\cot x-\sec\left(\frac{\pi}{2}+x\right)\right\}\left\{1+\cot x+\sec\left(\frac{\pi}{2}+x\right)\right\}=2\cot x\)

Express each of the following as the sum or difference of sine or cosine:
cos7ፀ sin3ፀ

Express \(\tan ^{ -1 } \left( \frac { \cos x-\sin x }{ \cos x+\sin x } \right) ,0<x<\pi \), in the simplest form.

Show that \(\sin^{-1}\left(\frac{-3}{5}\right)+\sin^{-1}\left(\frac{-8}{17}\right)=\cos^{-1}\left(\frac{84}{85}\right)\)

Prove that \(\sqrt3\)cosec 20^o-sec 20^o=4

Find the values of each of the following trigonometric ratios.
cos(- 210^o)

Show that \(\cos^{-1}\left(\frac{12}{13}\right)+\sin^{-1}\left(\frac35\right)=\sin^{-1}\left(\frac{56}{65}\right)\)

Convert the following into the product of trigonometric functions
cos4\(\alpha\)-cos8\(\alpha\)

Prove that \(\frac{\sin5x-2\sin3x+sinx}{\cos5x-\cos x}=\tan x\)

Show that \(\tan\left(\frac{\pi}{3}+x\right)\tan\left(\frac{\pi}{3}-x\right)=\frac{2\cos2x+1}{2\cos2x-1}\)

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