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#### Inverse Trigonometric Functions Two Marks Questions

12th Standard EM

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. State the reason for cos-1$[cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.$

2. Is cos-1(-x)=$\pi$-cos−1(x) true? Justify your answer.

3. Find the principal value of cos-1$(\frac{1}{2})$.

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

5. If cot-1$\frac{1}{7}=\theta$, find the value of cos$\theta$.

6. Find the value of
${ tan }^{ -1 }\left( \sqrt { 3 } \right) -{ sec }^{ -1 }(-2)$

7. Find all the values of x such that
-8$\pi$$\le x\le$-8$\pi$ and sin x=-1

8. Find the value of
tan (tan−1(-0.2021))

9. Simplify
sin-1[sin10]

10. Find the value of
$cos\left[ \frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 1 }{ 8 } \right) \right]$

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

12. If ${ sin }^{ -1 }\left( \cfrac { 1 }{ 2 } \right) ={ tan }^{ -1 }x$ then find the value of x,

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

14. Prove that $2{ tan }^{ -1 }\left( \cfrac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \cfrac { 12 }{ 5 } \right)$

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