Prove that...?

(1+2sinxcosx)/(sinx+cosx)=sinx+cosx

1 Answer
Feb 21, 2018

"Please see proof below."

Explanation:

"We are asked to prove:"

\qquad \qquad \qquad \qquad \qquad { 1+ 2 sinx cosx } / { sinx + cosx } \ = \ sinx + cosx.

"Looking at the LHS, we have the following:"

\qquad { 1+ 2 sinx cosx } / { sinx + cosx } \ = \ { ( sin^2x + cos^2x )+ 2 sinx cosx } / { sinx + cosx }

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ { sin^2x + 2 sinx cosx + cos^2x } / { sinx + cosx }

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ ( sinx + cosx )^2 / { sinx + cosx }

\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ sinx + cosx.

\qquad :. \qquad \qquad \qquad \qquad { 1+ 2 sinx cosx } / { sinx + cosx } \ = \ sinx + cosx. \qquad \qquad \qquad \qquad \ \ (!)