Prove the following identies using basic pythagorean sum and

Prove the following identies using basic, pythagorean, sum and difference or double/half angle identities. Show your work.

sin(+)/tan + tan=cos cos

Solution

sin(+)/tan + tan=cos cos

LHS = [sin(+)]/(sin/cos + sin/cos)

= [sin(+)]*cos*cos/(sincos + cossin) = sin(+)*cos*cos/sin(+)

= cos*cos = RHS