Question

Prove that this are equal:sin(x+y)*cos(x-y)+cos(x+y)*cos(x-y) / cos(x+y)*cos(x-y)-sin(x+y)*sin(x-y) is equal with tg2x ?

Answer 1

Please see below.

Explanation:

`(sin(x+y)*cos(x-y)+cos(x+y)*cos(x-y))/(cos(x+y)*cos(x+y)-sin(x+y)*sin(x-y))`

Let `A=x+y` and `B=x-y`, then the above becomes

`(sinAcosB+cosAsinB)/(cosAcosB-sinAsinB)`

= `sin(A+B)/cos(A+B)`

= `sin(x+y+x-y)/cos(x+y+x-y)`

= `(sin2x)/(cos2x)`

= `tan2x`