Question

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

Answer 1

`tan(x+y)=1`

Explanation:

`color(blue)(Ascolor(white)(.)sin(90^@-theta)=costheta)`

`sin(2x-20^@)=cos(2y+20^@)` can be written as

or `sin(2x-20^@)=sin(90^@-2y-20^@)`

or `sin(2x-20^@)=sin(70^@-2y)`

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

or `2x-20^@=70^@-2y`

or `2x+2y=90^@`

and so `x+y=45^@`

Hence, `tan(x+y)=tan45^@=tan45^@=1color(white)(x)color(brown)(Ans.)`