Question

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$☛ \: cos (\frac{\pi}{4} - x) \: cos{\pi}{4} - y) - \: sin( \frac{\pi}{4} )sin( \frac{\pi}{4} - y) = sin(x + y)$


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Answer 1

Step-by-step explanation:

☠️Aɴsᴡᴇʀ☠️

༒cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)cos(pi/4-y)=sin(x+y)

L.H.S:-

cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)

We know that, (If you dont know)

cos(A)cos(B)-sin(A)sin(B)=cos(A+B)

putting the above formula in the equation, we got

cos(pi/4+pi/4-x-y)

cos(pi/2-(x+y))

we also know that, (if you dont know)

cos(pi/2-theta)= sin(theta)

So, from the above equation, we got

cos(pi/2-(x+y))= sin(x+y)= R.H.S༒

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