Rewrite cos theta sin thetacos theta cos theta sin thetas

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

Solution

(cos theta + sin theta)/ cos theta + ( cos theta- sin theta)/sin theta

(sin theta(cos theta+ sin theta) + cos theta(cos theta-sin theta))/ (sintheta cos theta)

(sintheta costheta+sin^2theta+cos^2theta-sintheta costheta)/sintheta costheta

(sin^2theta + cos^2theta)/ sintheta costheta

1/(sintheta costheta)