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

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

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Application +4 | -1

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

, then the value

\left( \mathrm{s} \right)

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

is, (are)

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because solving the given trigonometric equation leads to

\cos (\theta - \frac{\pi}{4}) = \pm \frac{1}{2\sqrt{2}}

for specific values of n.

Practice All Chapter MCQs →

\sin \,\,x\,\,\;cos\,\,3x = \sin \,\,3x\,\,\cos \,\,5x

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

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

x,\,\,y \in \left[ {0,10} \right]

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

\mathrm{X}

\theta \rightarrow \frac{\pi}{2}

\sin x+\cos x=\frac{\sqrt{7}}{2}

x \in\left[0, \frac{\pi}{4}\right]

\tan \frac{x}{2}

\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}

0 < x < \pi

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

\tan x