JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Application +4 | -1

\tan \alpha=\sqrt{ a}

, where

a

is a rational number which is not a perfect square, then which of the following is a rational number?

View answer and explanation

Correct option: C

\cos 2 \alpha

Option C (

\cos 2 \alpha

) is correct because

\cos 2 \alpha

can be expressed as

\frac{{1-\tan^2 \alpha}}{{1+\tan^2 \alpha}}

, which results in a rational number when

\tan \alpha = \sqrt{{a}}

and

a

is rational.

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