(A) Given,$\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$ $\Rightarrow \tan (\pi \cos \theta)=\tan \left(\frac{\pi}{2}-\pi \sin \theta\right)$ $\Right

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(A) Given,$\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$ $\Rightarrow \tan (\pi \cos \theta)=\tan \left(\frac{\pi}{2}-\pi \sin \theta\right)$ $\Rightarrow \pi \cos \theta=\frac{\pi}{2}-\pi \sin \theta$ $\Rightarrow \cos \theta+\sin \theta=\frac{1}{2}$ Dividing both sides by $\sqrt{2}$: $\Rightarrow \frac{1}{\sqrt{2}} \cos \theta+\frac{1}{\sqrt{2}} \sin \theta=\frac{1}{2 \sqrt{2}}$ $\Rightarrow \cos \theta \cos \frac{\pi}{4}+\sin \theta \sin \frac{\pi}{4}=\frac{1}{2 \sqrt{2}}$ $\Rightarrow \cos \left(\theta-\frac{\pi}{4}\right)=\frac{1}{2 \sqrt{2}}$

Class 11 Mathematics Trigonometrical Equations Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

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

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A
$\frac{1}{2 \sqrt{2}}$
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{2}$
D
$\frac{1}{4}$

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Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

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