If tan (pi cos theta ) = cot (pi sin theta ), | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given $	an (\pi \cos 	heta ) = \cot (\pi \sin 	heta )$.Using the identity $\cot(x) = 	an\left(\frac{\pi}{2} - xight)$,we get:$	an (\pi \cos

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Given $	an (\pi \cos 	heta ) = \cot (\pi \sin 	heta )$.Using the identity $\cot(x) = 	an\left(\frac{\pi}{2} - xight)$,we get:$	an (\pi \cos 	heta ) = 	an \left( \frac{\pi}{2} - \pi \sin 	heta ight)$.This implies $\pi \cos 	heta = \frac{\pi}{2} - \pi \sin 	heta + n\pi$ for some integer $n$.Taking $n=0$,we have $\cos 	heta + \sin 	heta = \frac{1}{2}$.Multiply both sides by $\frac{1}{\sqrt{2}}$:$\frac{1}{\sqrt{2}} \cos 	heta + \frac{1}{\sqrt{2}} \sin 	heta = \frac{1}{2\sqrt{2}}$.Using the formula $\cos(A-B) = \cos A \cos B + \sin A \sin B$,where $A = 	heta$ and $B = \frac{\pi}{4}$:$\cos \left( 	heta - \frac{\pi}{4} ight) = \frac{1}{2\sqrt{2}}$.

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

Similar Questions

The number of all possible integral values of $n > 2$ such that $\sin \frac{\pi}{2n} + \cos \frac{\pi}{2n} = \frac{\sqrt{n}}{2}$ is:

If $\sin (y+z-x), \sin (z+x-y)$ and $\sin (x+y-z)$ are in $A$.$P$.,then

If $\cos \left(\frac{\pi}{4}-x\right) \cos 2 x+\sin x \sin 2 x \sec x = \cos x \sin 2 x \sec x+\cos \left(\frac{\pi}{4}+x\right) \cos 2 x$,then a possible value of $\sec x$ is

If $\sin (\theta + \alpha ) = a$ and $\sin (\theta + \beta ) = b,$ then $\cos 2(\alpha - \beta ) - 4ab\cos (\alpha - \beta )$ is equal to

The number of pairs $(x, y)$ satisfying the equations $\sin x + \sin y = \sin (x + y)$ and $|x| + |y| = 1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module