Rewrite sin theta cos thetasin theta cos theta sin thetac

Rewrite sin theta + cos theta/sin theta - cos theta - sin theta/cos theta over a common denominator. Type your answer in terms of sine and/or cosine. sin theta + cos theta/sin theta - cos theta - sin theta/cos theta = (Simplify your answer.)

Solution

[(sin+cos)_/sin]-[(cos-sin)_/cos]

=[[(sin+cos)cos]-[(cos-sin)sin]]_/(sincos)

=[(sincos+cos²)-(sincos-sin²)]_/(sincos)

=[sincos+cos²-sincos+sin²]_/(sincos)

=(cos²+sin²)_/(sincos)

=1_/(sincos)

therefore [(sin+cos)_/sin]-[(cos-sin)_/cos]=1_/(sincos)