Prove that...?

Question

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

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Answer 1 · 2018-02-21T00:11:52

# "Please see proof below." #

# "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 \ \ (!) #