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.)#