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JEE • MATHEMATICS • INVERSE TRIGONOMETRY

Inverse trigonometry practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 361-365 of 365 questions

361 Easy

361 of 365

Application +4 | -1

{\sin ^{ - 1}}x + {\sin ^{ - 1}}y + {\sin ^{ - 1}}z = \frac{{3\pi }}{2},

then the value of

{x^{100}} + {y^{100}} + {z^{100}} - \frac{9}{{{x^{101}} + {y^{101}} + {z^{101}}}}

View answer and explanation

Correct option: A

Option A (0) is correct because if

{\sin ^{ - 1}}x + {\sin ^{ - 1}}y + {\sin ^{ - 1}}z = \frac{{3\pi }}{2}

, then

x=y=z=1

, and substituting these values into the expression yields 0.

362 Easy

362 of 365

Application +4 | -1

If the inverse trigonometric functions take principal values, then

{\cos ^{ - 1}}\left( {\frac{3}{{10}}\cos \left( {{{\tan }^{ - 1}}\left( {\frac{4}{3}} \right)} \right) + \frac{2}{5}\sin \left( {{{\tan }^{ - 1}}\left( {\frac{4}{3}} \right)} \right)} \right)

is equal to:

View answer and explanation

Correct option: C

\frac{\pi }{3}

Option C (

\frac{\pi }{3}

) is correct because after simplifying the trigonometric expressions inside the inverse cosine, the result is cos⁻¹(1/2), which equals π/3.

363 Easy

363 of 365

Application +4 | -1

The value of

{\sin ^{ - 1}}\left\{ {\cos \left( {4095^\circ } \right)} \right\}

is equal to

View answer and explanation

Correct option: C

- \frac{\pi }{4}

Option C (

- \frac{\pi }{4}

) is correct because it is the simplified value of the given expression after applying trigonometric identities and considering the range of the inverse sine function.

364 Easy

364 of 365

Application +4 | -1

The value of

\sec \left[ {{{\tan }^{ - 1}}\left( {\frac{{b + a}}{{b - a}}} \right) - {{\tan }^{ - 1}}\left( {\frac{a}{b}} \right)} \right]

View answer and explanation

Correct option: B

\sqrt 2

Option B (

\sqrt 2

) is correct because simplifying the expression using the tangent subtraction formula and then finding the secant of the result gives this value.

365 Easy

365 of 365

Analyzing +4 | -1

x \in \left( { - \frac{\pi }{2},\frac{\pi }{2}} \right),

then the value of

{\tan ^{ - 1}}\left( {\frac{{\tan x}}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{{3\sin 2x}}{{5 + 3\cos 2x}}} \right)

View answer and explanation

Correct option: D

x

Option D (

x

) is correct because the expression simplifies to

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

, which equals

x

within the given interval.

Revision notes and key takeaways

Review INVERSE TRIGONOMETRY in your textbook or class notes, then use this set to check your understanding.

Showing 361-365 of 365 questions

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