If $\tan \,({\rm{\pi }}\cos \,\,{\rm{\theta }}) = \cot \,({\rm{\pi }}\,\,\sin \,\,{\rm{\theta }})$, then the value of $\cos \,\,\left( {{\rm{\theta }} - \frac{{\rm{\pi }}}{4}} \right)$ is equal to

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

\tan \,(\mathrm{\pi }\cos \,\,\mathrm{\theta }) = \cot \,(\mathrm{\pi }\,\,\sin \,\,\mathrm{\theta })

, then the value of

\cos \,\,\left( {\mathrm{\theta } - \frac{\mathrm{\pi }}{4}} \right)

is equal to

View answer and explanation

Correct option: A

\frac{1}{{2\,\sqrt 2 }}

The correct answer is A (

\frac{1}{{2\sqrt 2 }}

) because solving the given equation leads to

\sin \theta + \cos \theta = \frac{1}{2}

, which simplifies to the desired expression.

Practice All Chapter MCQs →

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\left[ {0,\;\,\frac{\pi }{2}} \right]

\left( {x,\,y} \right)

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\left( {\sqrt {{{\sin }^2} - \sin \,\,x + \frac{1}{2}} } \right){2^{{{\sec }^2}y}}\,\, \cdot \,\, \le 1

\mathrm{X}

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\tan \frac{x}{2}

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0 < x < \pi

\cos x+\sin x=\frac{1}{2}

\tan x