JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Analyzing +4 | -1

Let

\theta \in \left( {0,\;\,\frac{\pi }{4}} \right)

and

{t_1} = {\left( {\tan \,\,\theta } \right)^{\tan \theta }},\,\;{t_2} = {\left( {\tan \,\,\theta } \right)^{\cot \theta }},\;\,{t_3} = {\left( {\cot \,\,\theta } \right)^{\tan \theta }}

and

{t_4} = {\left( {\cot \,\,\theta } \right)^{\tan \theta }}

, then

View answer and explanation

Correct option: B

{t_4} > {t_3} > {t_1} > {t_2}

Option B (

{t_4} > {t_3} > {t_1} > {t_2}

) is correct because when

\theta \in (0, \frac{\pi}{4})

\tan \theta < 1

and

\cot \theta > 1

, leading to the given inequality.

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