Question

Given $tan\left(\pi cos\theta \right)=cot\left(\pi sin\theta \right),$ then the value of $cos(\theta -\frac{1}{4}\pi )$ will be-

• A. $\frac{1}{2\sqrt{2}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{3\sqrt{2}}$
• D. $\frac{1}{4\sqrt{2}}$

Answer 1

The correct option is A $\frac{1}{2\sqrt{2}}$

$tan\left(\pi cos\theta \right)=cot\left(\pi sin\theta \right)=tan\left[\right(\frac{\pi }{2})-\pi sin\theta ]\therefore \pi cos\theta =\left(\frac{\pi }{2}\right)-\pi sin\theta cos\theta +sin\theta =\left(\frac{1}{2}\right)cos\theta \times \left(\frac{1}{\sqrt{2}}\right)+sin\theta \times \left(\frac{1}{\sqrt{2}}\right)=\left(\frac{1}{2\sqrt{2}}\right)cos(\theta -(\frac{\pi }{4}\left)\right)=\left(\frac{1}{2\sqrt{2}}\right)$