If 2 ${\tan ^{ - 1}}\left( {{\rm{cos}}\;x} \right) = {\tan ^{ - 1}}\left( {2\;{\rm{cosec}}\;x} \right),\;$ then the value of $x$ is

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

If 2

{\tan ^{ - 1}}\left( {\mathrm{cos}\;x} \right) = {\tan ^{ - 1}}\left( {2\;\mathrm{cosec}\;x} \right),\;

then the value of

x

View answer and explanation

Correct option: B

\frac{\pi }{4}

Option B is correct because solving the equation

2{\tan ^{ - 1}}(\cos x) = {\tan ^{ - 1}}(2\mathrm{cosec}\;x)

leads to

x = \frac{\pi }{4}

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