Question

if sin(πcosx)=cos(πsinx) then find cos(x+π/4)

Answer 1

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Answer 2

Given:

$\sin \pi \cos x$= $\cos \pi \sin \pi$

We have to find the value of $\cos (x+\dfrac{\pi}{4} )$.

Solution:

∴ $\sin \pi \cos x$ = $\cos \pi \sin \pi$

⇒ $\sin \pi \cos x$ - $\cos \pi \sin \pi$ = 0

Using the trigonometric identity:

$\sin (A-B)$= $\sin A \cos B$ - $\cos A\sin B$  

$\sin (\pi-x)$ = 0

⇒ $\sin (\pi-x)$ = $\sin 0$ =

⇒ π - x = 0

⇒ x = π

∴ $\cos (\pi+\dfrac{\pi}{4} )$

= $-\cos \dfrac{\pi}{4}$

= - $\dfrac{1}{\sqrt{2}}$

Thus, $\cos (x+\dfrac{\pi}{4} )$ =  - $\dfrac{1}{\sqrt{2}}$