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

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Answer 1 · 2017-12-20T06:41:12

#tan(x+y)=1#

#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.)#