#### Trigonometry Three Marks Questions

11th Standard

Reg.No. :
•
•
•
•
•
•

Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. Find all other trigonometrical ratios if $\sin x=\frac{-2\sqrt6}{5}$ and x lies in III quadrant?

2. Prove that $\sin^2\frac{\pi}{6}+\cos^2\frac{\pi}{3}-\tan^2\frac{\pi}{4}=-\frac12$

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

4. Write $\tan ^{ -1 }{ \left( \frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \right) } ,\left| x \right| >1$ in the simplest form.

5. Prove that $\frac{\sin(x+y)}{\sin(x-y)}=\frac{\tan x+\tan y}{\tan x-\tan y}$

6. If $\alpha$ and $\beta$ are acute angles such that $\tan\alpha=\frac{m}{m+1}$ and $\tan\beta=\frac{1}{2m+1}$, prove that $\alpha+\beta=\frac{\pi}{4}$

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

8. Prove that $\frac{\sin5x+\sin3x}{\cos5x+\cos3x}=\tan4x$

9. Prove that $\frac{\sin5x-2\sin3x+sinx}{\cos5x-\cos x}=\tan x$

10. Show that $\cos^{-1}\left(\frac{3}{5}\cos x+\frac45\sin x\right)=x-\tan^{-1}\left(\frac43\right)$