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JEE • MATHEMATICS • TRIGONOMETRY RATIOS

Trigonometry ratios practice · Mixed difficulty

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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 391-394 of 394 questions

391 Easy

391 of 394

Application +4 | -1

\mathrm{sec}\,\mathrm{\theta \; + }\,\mathrm{tan}\,\mathrm{\theta } = 1

, then root of the equation

\left( {a - 2b + c} \right){x^2}\,\, + \,\,\left( {b - 2c + a} \right)x\,\, + \,\,\left( {c - 2a + b} \right) = 0

View answer and explanation

Correct option: A

\sec \,\,\mathrm{\theta }

Option A (

\sec \theta

) is correct because one root of the quadratic equation is 1, and given the condition

\sec \theta + \tan \theta = 1

, it follows that

\sec \theta = 1

392 Medium

392 of 394

Analyzing +4 | -1

The value of

{\cos ^2}A\;{\left( {3 - 4\,\,{{\cos }^2}A} \right)^2} + {\sin ^2}A\;{\left( {3 - 4\,\,{{\sin }^2}\,A} \right)^2}

is equal to

View answer and explanation

Correct option: C

\mathrm{1}

Option C (1) is correct because the expression simplifies to 1 after applying trigonometric identities and algebraic manipulation.

393 Easy

393 of 394

Understanding +4 | -1

\alpha, \beta, \gamma

are the angles which a half ray makes with the positive directions of the axes, then

\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma

is equal to

View answer and explanation

Correct option: B

Option B (2) is correct because

\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 2

when

\alpha, \beta, \gamma

are the angles a half ray makes with the positive directions of the axes.

394 Medium

394 of 394

Application +4 | -1

\;\tan \,\,\mathrm{\theta },\,\,2\tan \mathrm{\theta } + 2,\;\,3\tan \mathrm{\theta } + 3\;

are in GP, then the value of

\frac{{7 - 5\,\cot \mathrm{\theta }}}{{9 - 4\,\sqrt {{{\sec }^2}\mathrm{\theta } - 1} }}

View answer and explanation

Correct option: C

\frac{{33}}{{100}}

Option C (33/100) is the correct answer because it is obtained by solving the given GP condition for tan θ and substituting it into the expression.

Revision notes and key takeaways

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

Showing 391-394 of 394 questions

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