Prove the identity
1-tan(x)tan(y)) = (cos(x+y)/cos(x)cos(y)

Question

Prove the identity 
1-tan(x)tan(y)) = (cos(x+y)/cos(x)cos(y)

jamesj · Answer

What is cos(x+y) equal to?  I.e., expand it out.

anonymous · Answer

Using the formula        cos(A+B)=cos A cos B - sin A sin B

             cos (x + y)      cos(x)cos(y) - sin(x)sin(y)      cos(x)cos(y)        sin(x)sin(y)
RHS = ---------- = ---------------------- = ------------ - ------------
            cos(x)cos(y)               cos(x)cos(y)                  cos(x)cos(y)         cos(x)cos(y)

            sin(x)        sin(y)
= 1 - ------- * ------ = 1 - tan(x)*tan(y) = 1 - tan(x)tan(y) = LHS
            cos(x)       cos(y)