Question

If sin (πcos theta) = cos(πsin theta), then cos (theta + π/4) is equal to

Answer 1

Answer:

$\frac{ \sqrt{3} + 1 }{2 \sqrt{2} }$

Step-by-step explanation:

Given that,

$\sin(\pi \cos( \alpha ) ) = \cos(\pi \sin( \alpha ) )$

$= \cos(\pi \sin( \alpha ) ) = \cos( \frac{\pi}{2} - \pi \cos( \alpha ) ) ........{ \sin(\pi \cos( \alpha ) ) = \cos( \frac{\pi}{2} - \pi \cos( \alpha ) )$

$= \pi \sin( \alpha ) = 2n\pi + \frac{\pi}{2} - \pi \cos( \alpha ) \: \: or \: \: \pi \sin( \alpha ) = 2n\pi - \frac{\pi}{2} + \pi \cos( \alpha )$

$= \pi( \sin( \alpha ) + \cos( \alpha ) ) = 2n\pi + \frac{\pi}{2} \: \: or \: \: \pi( \sin( \alpha ) - \cos( \alpha ) ) = 2n\pi - \frac{\pi}{2}$

$= \sin( \alpha ) + \cos( \alpha ) = 2n + \frac{1}{2} \: \:.....(i) or \: \: \sin( \alpha ) - \cos( \alpha ) = 2n - \frac{1}{2}.....(ii)$

subtracting (ii) from (i), we get