If x and y are acute angles and sin(2x20)=cos(2y+20), what is tan(x+y)?

1 Answer

tan(x+y)=1

Explanation:

As.sin(90θ)=cosθ

sin(2x20)=cos(2y+20) can be written as

or sin(2x20)=sin(902y20)

or sin(2x20)=sin(702y)

and as x,y and (x+y) are acute angles

or 2x20=702y

or 2x+2y=90

and so x+y=45

Hence, tan(x+y)=tan45=tan45=1xAns.