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#### Inverse Trigonometric Functions Model Question Paper

12th Standard EM

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 40
7 x 1 = 7
1. If $\\ \\ \\ { cot }^{ -1 }\left( \sqrt { sin\alpha } \right) +{ tan }^{ -1 }\left( \sqrt { sin\alpha } \right) =u$, then cos2u is equal to

(a)

tan2$\alpha$

(b)

0

(c)

-1

(d)

tan2$\alpha$

2. If |x|$\le$1, then 2tan-1 x-sin-1 $\frac{2x}{1+x^2}$ is equal to

(a)

tan-1x

(b)

sin-1x

(c)

0

(d)

$\pi$

3. If sin-1 $\frac{x}{5}+ cosec^{-1}\frac{5}{4}=\frac{\pi}{2}$, then the value of x is

(a)

4

(b)

5

(c)

2

(d)

3

4. sin(tan-1x), |x|<1 ia equal to

(a)

$\frac{x}{\sqrt{1-x^2}}$

(b)

$\frac{1}{\sqrt{1-x^2}}$

(c)

$\frac{1}{\sqrt{1+x^2}}$

(d)

$\frac{x}{\sqrt{1+x^2}}$

5. The number of solutions of the equation ${ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 }$

(a)

2

(b)

3

(c)

1

(d)

none

6. $sin\left\{ 2{ cos }^{ -1 }\left( \cfrac { -3 }{ 5 } \right) \right\} =$

(a)

$\cfrac { 6 }{ 15 }$

(b)

$\cfrac { 24 }{ 25 }$

(c)

$\cfrac { 4 }{ 5 }$

(d)

$\cfrac { -24 }{ 25 }$

7. The value of tan $\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right)$ is ______

(a)

$\cfrac { 19 }{ 8 }$

(b)

$\cfrac { 8 }{ 19 }$

(c)

$\cfrac { 19 }{ 12 }$

(d)

$\cfrac { 3 }{ 4 }$

8. 1 x 2 = 2
9. (1) cot(cot-1(+600)) = -600
(2) cot(cot-1(1782)) = 1782
(3) $cot\left( { cot }^{ -1 }\left( \cfrac { -17 }{ 9 } \right) \right) =\cfrac { -17 }{ 9 }$
(4) $cot({ cot }^{ -1 }\left( \sqrt { 3 } \right) =\sqrt { 3 }$

10. 5 x 2 = 10
11. Find the principal value of
${ Sin }^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right)$

12. Find all the values of x such that
-10$\pi$$\le x\le$10$\pi$ and sin x=0

13. Find the period and amplitude of
y=4sin(−2x)

14. Find the principal value of ${ cos }^{ -1 }\left( \cfrac { -1 }{ 2 } \right)$

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

16. 2 x 3 = 6
17. Find
i)  tan−1($-\sqrt3$)
ii)  tan−1$(tan\frac{3\pi}{5})$
iii) tan(tan-1−(2019))

18. Solve: cos(tan-1x) = $sin\left( { cot }^{ -1 }\cfrac { 3 }{ 4 } \right)$

19. 3 x 5 = 15
20. Find (i) cos-1 $(-\frac{1}{\sqrt2})$
ii) cos-1$(cos(-\frac{\pi}{3}))$
iii) cos-1$(cos(-\frac{7\pi}{6}))$

21. Find the principal value of
sec−1(−2).

22. If ${ tan }^{ -1 }\left( \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right) =a$ than prove that x2=sin2a