# Inverse trigonometrical functions Test 1

Total Questions:50 Total Time: 60 Min

Remaining:

## Questions 1 of 50

Question:$$\tan \left[ {{{\sec }^{ - 1}}\sqrt {1 + {x^2}} } \right] =$$

$$\frac{1}{x}$$

$$x$$

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

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

## Questions 2 of 50

Question:$${\sec ^{ - 1}}[\sec ( - {30^o})] =$$

$$- {60^o}$$

$$- {30^o}$$

$${30^o}$$

$${150^o}$$

## Questions 3 of 50

Question:$${\tan ^{ - 1}}\left[ {\frac{{\cos x}}{{1 + \sin x}}} \right] =$$

$$\frac{\pi }{4} - \frac{x}{2}$$

$$\frac{\pi }{4} + \frac{x}{2}$$

$$\frac{x}{2}$$

$$\frac{\pi }{4} - x$$

## Questions 4 of 50

Question:$${\tan ^{ - 1}}\frac{1}{{\sqrt {{x^2} - 1} }} =$$

$$\frac{\pi }{2} + {\rm{cose}}{{\rm{c}}^{ - 1}}x$$

$$\frac{\pi }{2} + {\sec ^{ - 1}}x$$

$${\rm{cose}}{{\rm{c}}^{ - 1}}x$$

$${\sec ^{ - 1}}x$$

## Questions 5 of 50

Question:The principal value of $${\sin ^{ - 1}}\left( { - \frac{1}{2}} \right)$$is

$$\frac{\pi }{3}$$

$$\frac{\pi }{6}$$

$$- \frac{\pi }{3}$$

$$- \frac{\pi }{6}$$

## Questions 6 of 50

Question:$${\sec ^2}({\tan ^{ - 1}}2) + {\rm{cose}}{{\rm{c}}^2}({\cot ^{ - 1}}3) =$$

5

13

15

6

## Questions 7 of 50

Question:$${\sin ^{ - 1}}\left[ {x\sqrt {1 - x} - \sqrt x \sqrt {1 - {x^2}} } \right] =$$

$${\sin ^{ - 1}}x + {\sin ^{ - 1}}\sqrt x$$

$${\sin ^{ - 1}}x - {\sin ^{ - 1}}\sqrt x$$

$${\sin ^{ - 1}}\sqrt x - {\sin ^{ - 1}}x$$

None of these

## Questions 8 of 50

Question:The principal value of $${\sin ^{ - 1}}\left( { - \,\,\frac{{\sqrt 3 }}{2}} \right)$$is

$$\frac{{ - 2\pi }}{3}$$

$$\frac{{ - \pi }}{3}$$

$$\frac{{ - 2\pi }}{3}$$

$$\frac{{5\pi }}{3}$$

## Questions 9 of 50

Question:$$\cot \,\,\left[ {{{\cos }^{ - 1}}\left( {\frac{7}{{25}}} \right)} \right] =$$

$$\frac{{25}}{{24}}$$

$$\frac{{25}}{7}$$

$$\frac{{24}}{{25}}$$

None of these

## Questions 10 of 50

Question:If $$\frac{\pi }{2} \le x \le \frac{{3\pi }}{2},$$then$${\sin ^{ - 1}}(\sin x)$$is equal to

x

$$- x$$

$$\pi + x$$

$$\pi - x$$

## Questions 11 of 50

Question:If $$\pi \le x \le 2\pi$$, then $${\cos ^{ - 1}}(\cos x)$$is equal to

x

$$- x$$

$$2\pi + x$$

$$2\pi - x$$

## Questions 12 of 50

Question:The value of $${\sin ^{ - 1}}(\sin 10)$$is

10

$$10 - 3\pi$$

$$3\pi - 10$$

None of these

## Questions 13 of 50

Question:The smallest and the largest values of $${\tan ^{ - 1}}\left( {\frac{{1 - x}}{{1 + x}}} \right){\rm{ }},\,\,0 \le x \le 1$$are

$$0,\,\,\pi$$

$$0,\,\frac{\pi }{4}$$

$$- \frac{\pi }{4},\frac{\pi }{4}$$

$$\frac{\pi }{4},\,\frac{\pi }{2}$$

## Questions 14 of 50

Question:If $$x$$takes non-positive permissible value, then $${\sin ^{ - 1}}x$$=

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

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

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

$$\pi - {\cos ^{ - 1}}\sqrt {1 - {x^2}}$$

## Questions 15 of 50

Question:$$\sin \left[ {\frac{\pi }{2} - {{\sin }^{ - 1}}\left( { - \frac{{\sqrt 3 }}{2}} \right)} \right] =$$

$$\frac{{\sqrt 3 }}{2}$$

$$- \frac{{\sqrt 3 }}{2}$$

$$\frac{1}{2}$$

$$- \frac{1}{2}$$

## Questions 16 of 50

Question:$$\sin [{\cot ^{ - 1}}(\cos {\tan ^{ - 1}}x)]$$=

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

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

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

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

## Questions 17 of 50

Question:If $$\sin ({\cot ^{ - 1}}(x + 1) = \cos ({\tan ^{ - 1}}x)$$, then x =

$$- \frac{1}{2}$$

$$\frac{1}{2}$$

0

$$\frac{9}{4}$$

## Questions 18 of 50

Question:$${\cos ^{ - 1}}\frac{4}{5} + {\tan ^{ - 1}}\frac{3}{5} =$$

$${\tan ^{ - 1}}\frac{{27}}{{11}}$$

$${\sin ^{ - 1}}\frac{{11}}{{27}}$$

$${\cos ^{ - 1}}\frac{{11}}{{27}}$$

None of these

## Questions 19 of 50

Question:$${\sin ^{ - 1}}x + {\sin ^{ - 1}}\frac{1}{x} + {\cos ^{ - 1}}x + {\cos ^{ - 1}}\frac{1}{x} =$$

$$\pi$$

$$\frac{\pi }{2}$$

$$\frac{{3\pi }}{2}$$

None of these

## Questions 20 of 50

Question:$$2{\tan ^{ - 1}}\frac{1}{3} + {\tan ^{ - 1}}\frac{1}{2} =$$

$${90^o}$$

$${60^o}$$

$${45^o}$$

$${\tan ^{ - 1}}2$$

## Questions 21 of 50

Question:$${\tan ^{ - 1}}\frac{{a - b}}{{1 + ab}} + {\tan ^{ - 1}}\frac{{b - c}}{{1 + bc}} =$$

$${\tan ^{ - 1}}a - {\tan ^{ - 1}}b$$

$${\tan ^{ - 1}}a - {\tan ^{ - 1}}c$$

$${\tan ^{ - 1}}b - {\tan ^{ - 1}}c$$

$${\tan ^{ - 1}}c - {\tan ^{ - 1}}a$$

## Questions 22 of 50

Question:If $${\tan ^{ - 1}}2x + {\tan ^{ - 1}}3x = \frac{\pi }{4}$$, then x =

1

$$\frac{1}{6}$$

$$- 1,\,\frac{1}{6}$$

None of these

## Questions 23 of 50

Question:If $${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$$, then x =

1/3

1/4

3

4

## Questions 24 of 50

Question:$$2{\sin ^{ - 1}}\frac{3}{5} + {\cos ^{ - 1}}\frac{{24}}{{25}} =$$

$$\frac{\pi }{2}$$

$$\frac{{2\pi }}{3}$$

$$\frac{{5\pi }}{3}$$

None of these

## Questions 25 of 50

Question:$$\cos \left[ {{{\tan }^{ - 1}}\frac{1}{3} + {{\tan }^{ - 1}}\frac{1}{2}} \right] =$$

$$\frac{1}{{\sqrt 2 }}$$

$$\frac{{\sqrt 3 }}{2}$$

$$\frac{1}{2}$$

$$\frac{\pi }{4}$$

## Questions 26 of 50

Question:$${\tan ^{ - 1}}x + {\cot ^{ - 1}}(x + 1) =$$

$${\tan ^{ - 1}}({x^2} + 1)$$

$${\tan ^{ - 1}}({x^2} + x)$$

$${\tan ^{ - 1}}(x + 1)$$

$${\tan ^{ - 1}}({x^2} + x + 1)$$

## Questions 27 of 50

Question:$${\cos ^{ - 1}}\frac{1}{2} + 2{\sin ^{ - 1}}\frac{1}{2}$$is equal to

$$\frac{\pi }{4}$$

$$\frac{\pi }{6}$$

$$\frac{\pi }{3}$$

$$\frac{{2\pi }}{3}$$

## Questions 28 of 50

Question:$${\tan ^{ - 1}}\frac{3}{4} + {\tan ^{ - 1}}\frac{3}{5} - {\tan ^{ - 1}}\frac{8}{{19}} =$$

$$\frac{\pi }{4}$$

$$\frac{\pi }{3}$$

$$\frac{\pi }{6}$$

None of these

## Questions 29 of 50

Question:$$4{\tan ^{ - 1}}\frac{1}{5} - {\tan ^{ - 1}}\frac{1}{{70}} + {\tan ^{ - 1}}\frac{1}{{99}} =$$

$$\frac{\pi }{2}$$

$$\frac{\pi }{3}$$

$$\frac{\pi }{4}$$

None of these

## Questions 30 of 50

Question:If $${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{{2\pi }}{3},$$then $${\cos ^{ - 1}}x + {\cos ^{ - 1}}y =$$

$$\frac{{2\pi }}{3}$$

$$\frac{\pi }{3}$$

$$\frac{\pi }{6}$$

$$\pi$$

## Questions 31 of 50

Question:$${\tan ^{ - 1}}\left( {\frac{1}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{2}{9}} \right) =$$

$$\frac{1}{2}{\cos ^{ - 1}}\left( {\frac{3}{5}} \right)$$

$$\frac{1}{2}{\sin ^{ - 1}}\left( {\frac{3}{5}} \right)$$

$$\frac{1}{2}{\tan ^{ - 1}}\left( {\frac{3}{5}} \right)$$

$${\tan ^{ - 1}}\left( {\frac{1}{2}} \right)$$

## Questions 32 of 50

Question:$${\tan ^{ - 1}}\left( {\frac{x}{y}} \right) - {\tan ^{ - 1}}\,\left( {\frac{{x - y}}{{x + y}}} \right)$$ is

$$\frac{\pi }{2}$$

$$\frac{\pi }{3}$$

$$\frac{\pi }{4}$$

$$\frac{\pi }{4}$$or $$- \frac{{3\pi }}{4}$$

## Questions 33 of 50

Question:If $$\tan (x + y) = 33$$and $$x = {\tan ^{ - 1}}3,$$then y will be

$$0.3$$

$${\tan ^{ - 1}}(1.3)$$

$${\tan ^{ - 1}}(0.3)$$

$${\tan ^{ - 1}}\left( {\frac{1}{{18}}} \right)$$

## Questions 34 of 50

Question:If $${\tan ^{ - 1}}\frac{{x - 1}}{{x + 1}} + {\tan ^{ - 1}}\frac{{2x - 1}}{{2x + 1}} = {\tan ^{ - 1}}\frac{{23}}{{36}},$$then x =

$$\frac{3}{4},\frac{{ - 3}}{8}$$

$$\frac{3}{4},\frac{3}{8}$$

$$\frac{4}{3},\frac{3}{8}$$

None of these

## Questions 35 of 50

Question:$${\tan ^{ - 1}}\frac{{{c_1}x - y}}{{{c_1}y + x}} + {\tan ^{ - 1}}\frac{{{c_2} - {c_1}}}{{1 + {c_2}{c_1}}} +$$ $${\tan ^{ - 1}}\frac{{{c_3} - {c_2}}}{{1 + {c_3}{c_2}}} + ... + {\tan ^{ - 1}}\frac{1}{{{c_n}}} =$$

$${\tan ^{ - 1}}\frac{y}{x}$$

$${\tan ^{ - 1}}yx$$

$${\tan ^{ - 1}}\frac{x}{y}$$

$${\tan ^{ - 1}}(x - y)$$

## Questions 36 of 50

Question:$$\sin \left\{ {{{\sin }^{ - 1}}\frac{1}{2} + {{\cos }^{ - 1}}\frac{1}{2}} \right\} =$$

0

1

2

1

## Questions 37 of 50

Question:$${\sin ^{ - 1}}\frac{4}{5} + 2{\tan ^{ - 1}}\frac{1}{3} =$$

$$\frac{\pi }{2}$$

$$\frac{\pi }{3}$$

$$\frac{\pi }{4}$$

None of these

## Questions 38 of 50

Question:$${\sin ^{ - 1}}x + {\cos ^{ - 1}}x$$ is equal to

$$\frac{\pi }{4}$$

$$\frac{\pi }{2}$$

1

1

## Questions 39 of 50

Question:The value of $${\sin ^{ - 1}}\left( {\frac{{\sqrt 3 }}{2}} \right) - {\sin ^{ - 1}}\left( {\frac{1}{2}} \right)$$is

$${45^0}$$

$${90^0}$$

$${15^0}$$

$${30^0}$$

## Questions 40 of 50

Question:If $${\cos ^{ - 1}}x + {\cos ^{ - 1}}y + {\cos ^{ - 1}}z = 3\pi ,$$then $$xy + yz + zx =$$

0

1

3

3

## Questions 41 of 50

Question:$$\cos {\rm{ }}\left[ {{{\cos }^{ - 1}}{\rm{ }}\left( {\frac{{ - 1}}{7}} \right) + {{\sin }^{ - 1}}{\rm{ }}\left( {\frac{{ - 1}}{7}} \right)} \right] =$$

$$- 1/3$$

0

$$1/3$$

$$4/9$$

## Questions 42 of 50

Question:The value of $$\tan \left[ {{{\sin }^{ - 1}}\left( {\frac{3}{5}} \right) + {{\cos }^{ - 1}}\left( {\frac{3}{{\sqrt {13} }}} \right)} \right]$$is

$$\frac{6}{{17}}$$

$$\frac{6}{{\sqrt {13} }}$$

$$\frac{{\sqrt {13} }}{5}$$

$$\frac{{17}}{6}$$

## Questions 43 of 50

Question:The value of $$\tan \left( {{{\tan }^{ - 1}}\frac{1}{2} - {{\tan }^{ - 1}}\frac{1}{3}} \right)$$is

$$5/6$$

$$7/6$$

$$1/6$$

$$1/7$$

## Questions 44 of 50

Question:If $${\cos ^{ - 1}}\sqrt p + {\cos ^{ - 1}}\sqrt {1 - p} + {\cos ^{ - 1}}\sqrt {1 - q} = \frac{{3\pi }}{4},$$ then the value of q is

1

$$\frac{1}{{\sqrt 2 }}$$

$$\frac{1}{3}$$

$$\frac{1}{2}$$

## Questions 45 of 50

Question:$$\frac{1}{2}{\cos ^{ - 1}}\left( {\frac{{1 - x}}{{1 + x}}} \right) =$$

$${\cot ^{ - 1}}\sqrt x$$

$${\tan ^{ - 1}}\sqrt x$$

$${\tan ^{ - 1}}x$$

$${\cot ^{ - 1}}x$$

## Questions 46 of 50

Question:$$\sin \left( {4{{\tan }^{ - 1}}\frac{1}{3}} \right) =$$

$$\frac{{12}}{{25}}$$

$$\frac{{24}}{{25}}$$

$$\frac{1}{5}$$

None of these

## Questions 47 of 50

Question:$$3{\tan ^{ - 1}}a$$is equal to

$${\tan ^{ - 1}}\frac{{3a + {a^3}}}{{1 + 3{a^2}}}$$

$${\tan ^{ - 1}}\frac{{3a - {a^3}}}{{1 + 3{a^2}}}$$

$${\tan ^{ - 1}}\frac{{3a + {a^3}}}{{1 - 3{a^2}}}$$

$${\tan ^{ - 1}}\frac{{3a - {a^3}}}{{1 - 3{a^2}}}$$

## Questions 48 of 50

Question:$$4{\tan ^{ - 1}}\frac{1}{5} - {\tan ^{ - 1}}\frac{1}{{239}}$$is equal to

$$\pi$$

$$\frac{\pi }{2}$$

$$\frac{\pi }{3}$$

$$\frac{\pi }{4}$$

## Questions 49 of 50

Question:If $$3{\sin ^{ - 1}}\frac{{2x}}{{1 - {x^2}}} - 4{\cos ^{ - 1}}\frac{{1 - {x^2}}}{{1 + {x^2}}} + 2{\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}} = \frac{\pi }{3}$$ then $$x$$ =

$$\sqrt 3$$

$$\frac{1}{{\sqrt 3 }}$$

1

None of these

## Questions 50 of 50

Question:The value of $$\sin \left( {2{{\tan }^{ - 1}}\left( {\frac{1}{3}} \right)} \right) + \cos ({\tan ^{ - 1}}2\sqrt 2 ) =$$

$$\frac{{16}}{{15}}$$
$$\frac{{14}}{{15}}$$
$$\frac{{12}}{{15}}$$
$$\frac{{11}}{{15}}$$