" /> -->

#### Inverse Trigonometric Functions - Two Marks Study Materials

12th Standard EM

Reg.No. :
•
•
•
•
•
•

Maths

Time : 01:00:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Find the principal value of sin-1(2), if it exists.

2. Find the period and amplitude of
y=sin 7x

3. Find the value of
$2{ cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) +{ sin }^{ -1 }\left( \frac { 1 }{ 2 } \right)$

4. Find the value of sec−1$\left( -\frac { 2\sqrt { 3 } }{ 3 } \right)$

5. Prove that $\frac{\pi}{2}\le sin^{-1}x+2 cos^{-1} x\le\frac{3\pi}{2}$.

6. Find the value of
i) $sin\left[ \frac { \pi }{ 3 } -{ sin }^{ 2 }\left( -\frac { 1 }{ 2 } \right) \right]$

7. Prove that tan-1 x+tan-1 z=tan-1$\left[ \frac { x+y+z-xyz }{ 1-xy-yz-zx } \right]$

8. Find the value of
${ cos }^{ -1 }\left( cos\frac { \pi }{ 7 } cos\frac { \pi }{ 17 } -sin\frac { \pi }{ 17 } sin\frac { \pi }{ 17 } \right) .$

9. Find the principal value of
cot-1 $(\sqrt{3})$

10. Simplify
${ sec }^{ -1 }\left( sec\left( \frac { 5\pi }{ 3 } \right) \right)$

11. Simplify
sin-1[sin10]

12. Find the principal value of ${ tan }^{ -1 }\left( \cfrac { -1 }{ \sqrt { 3 } } \right)$

13. If ${ cot }^{ -1 }\left( \cfrac { 1 }{ 7 } \right) =\theta$ find the value of cos $\theta$

14. Prove that ${ tan }^{ -1 }\left( \cfrac { 1 }{ 7 } \right) +{ tan }^{ -1 }\left( \cfrac { 1 }{ 13 } \right) ={ tan }^{ -1 }\left( \cfrac { 2 }{ 9 } \right)$

15. Evaluate $sin\left( { cos }^{ -1 }\left( \cfrac { 1 }{ 2 } \right) \right)$