Question

How do you prove `cos(x+y)cosy + sin(x+y)siny = cosx`?

Answer 1

Please see below

Explanation:

Recall the trigonometrical identity

`cos(A-B)=cosAcosB+sinAsinB`

Putting `A=x+y` and `B=y`, we get

`cos(x+y-y)=cos(x+y)cosy+sin(x+y)siny`

or transposing LHS to RHS and vice-versa

`cos(x+y)cosy+sin(x+y)siny=cosx`