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

For $0 < \theta < \frac{\pi}{2}$,the solution$(s)$ of $\sum_{m=1}^6 \operatorname{cosec}\left(\theta+\frac{(m-1) \pi}{4}\right) \operatorname{cosec}\left(\theta+\frac{m \pi}{4}\right) = 4 \sqrt{2}$ is(are):

If $\sin \beta$ is the geometric mean between $\sin \alpha$ and $\cos \alpha,$ then $\cos 2\beta$ is equal to

Let $f_k(x) = \frac{1}{k}(\sin^k x + \cos^k x)$,where $x \in R$ and $k \ge 1$. Then $f_4(x) - f_6(x)$ is equal to

$\operatorname{sech}^{-1}(\sin \theta)$ is equal to

Number of real values of $x \in (0, \pi)$ for which $\frac{8}{3\sin x - \sin 3x} + 3\sin^2 x \le 5$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module