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

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

Question

(D) Given $	an (\pi \cos 	heta) = \cot (\pi \sin 	heta)$.We know that $\cot x = 	an \left(\frac{\pi}{2} - xight)$.So,$	an (\pi \cos 	heta) = \

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Given $	an (\pi \cos 	heta) = \cot (\pi \sin 	heta)$.We know that $\cot x = 	an \left(\frac{\pi}{2} - xight)$.So,$	an (\pi \cos 	heta) = 	an \left(\frac{\pi}{2} - \pi \sin 	hetaight)$.This implies $\pi \cos 	heta = n\pi + \frac{\pi}{2} - \pi \sin 	heta$ for some integer $n$.Dividing by $\pi$,we get $\cos 	heta + \sin 	heta = n + \frac{1}{2}$.Multiplying by $\frac{1}{\sqrt{2}}$,we get $\frac{1}{\sqrt{2}} \cos 	heta + \frac{1}{\sqrt{2}} \sin 	heta = \frac{n + 0.5}{\sqrt{2}}$.$\sin \left(\frac{\pi}{4} + 	hetaight) = \frac{n + 0.5}{\sqrt{2}}$.For the sine function to be within $[-1, 1]$,we test $n=0$: $\sin \left(\frac{\pi}{4} + 	hetaight) = \frac{0.5}{\sqrt{2}} = \frac{1}{2 \sqrt{2}}$.

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

Similar Questions

If $y^2+z^2=3yz$,$z^2+x^2=8zx$,and $x^2+y^2=4xy$,then the value of $\frac{y^2}{xz}+\frac{xz}{y^2}$ is

In triangles $ABC$ and $DEF$,$AB = DE$,$AC = EF$ and $\angle A = 2\angle E$. The two triangles will have the same area if angle $A$ is equal to:

Evaluate: $\sin 6^{\circ} + \sin 54^{\circ} + \sin 126^{\circ} + \cos 156^{\circ}$

If $\sum_{r=1}^{13} \left\{ \frac{1}{\sin \left(\frac{\pi}{4} + (r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4} + \frac{r\pi}{6}\right)} \right\} = a\sqrt{3} + b$,where $a, b \in \mathbb{Z}$,then $a^2 + b^2$ is equal to:

If $\sin x - \sin y = \frac{27}{65}$ and $\cos x - \cos y = \frac{-21}{65}$,then find the value of $\sin(x + y)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module