Solveeit Logo
Login

Question

Question: If \(\tan(\pi\cos\theta) = \cot(\pi\sin\theta),\) then the value of \(\cos\left( \theta - \frac{\pi}...

If tan⁡(πcos⁡θ)=cot⁡(πsin⁡θ),\tan(\pi\cos\theta) = \cot(\pi\sin\theta), then the value of cos⁡(θ−π4)=\cos\left( \theta - \frac{\pi}{4} \right) =

A

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

B

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

C

132\frac{1}{3\sqrt{2}}

D

142\frac{1}{4\sqrt{2}}

Answer

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

Explanation

Solution

tan⁡(πcos⁡θ)=tan⁡(π/2−πsin⁡θ)\tan(\pi\cos\theta) = \tan(\pi/2 - \pi\sin\theta)

⇒\Rightarrow cos⁡(θ−π4)=122.\cos\left( \theta - \frac{\pi}{4} \right) = \frac{1}{2\sqrt{2}}.