Question

If sine of the quantity x plus y end quantity equals radical 2 over 2 times sine of x plus radical 2 over 2 times cosine of x comma what is the value of y?

Answer 1

`\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y) \\\\\\ \sin(x+y)=\sin(x)\left( \cfrac{√(2)}{2} \right)\cos(x)\left( \cfrac{√(2)}{2} \right) \\\\[-0.35em] ~\dotfill\\\\ \cos(y)=\sin(y)=\cfrac{√(2)}{2}\hspace{5em}\cos\left( (\pi )/(4) \right)=\sin\left( (\pi )/(4) \right)=\cfrac{√(2)}{2}\hspace{5em}y=\cfrac{\pi }{4}`