SOLUTION: Prove the identity: (tanx+1)^2=(1+2 sinx cosx)/(cos^2)x

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Question 1131555: Prove the identity:
(tanx+1)^2=(1+2 sinx cosx)/(cos^2)x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28tan%28x%29%2B1%29%5E2=%281%2B2sin%28x%29%2A+cos%28x%29%29%2F%28cos%5E2%28x%29%29+
start with:
%28tan%28x%29%2B1%29%5E2

=tan%5E2%28x%29%2B2tan%28x%29%2B1.......tan%28x%29=sin%28x%29%2Fcos%28x%29

=sin%5E2%28x%29%2Fcos%5E2%28x%29%2B2%28sin%28x%29%2Fcos%28x%29%29%2B1

=

=%28sin%5E2%28x%29%2B2sin%28x%29cos%5E2%28x%29%2Bcos%5E2%28x%29%29%2Fcos%5E2%28x%29.......since sin%5E2%28x%29%2Bcos%5E2%28x%29=1, we have

=%281%2B2sin%28x%29cos%5E2%28x%29%29%2Fcos%5E2%28x%29