Rewrite over a common denominator sin theta cos thetacos th

Rewrite over a common denominator: sin theta + cos theta/cos theta + cos theta - sin theta/sin theta. Multiply and simplify: (sin theta + cos theta)(sin theta + cos theta) - 1/sin theta cos theta Factor and simplify: 3sin^2 theta + 4 sin theta + 1/sin^2 theta + 2 sin theta + 1

Solution

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

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

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

1/(sin theta cos theta)

7.5     (sin theta + cos theta)(sin theta + cos theta) - 1/sin theta cos theta

         (sin^2 theta + sin theta cos theta + sin theta cos theta + cos^2 theta)-1/sin theta cos theta

        (1 + sin 2 theta -1)/sin theta cos theta= sin 2theta/sin theta cos theta = 2