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

1 Answer

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.)