SOLUTION: Prove the identity: 2Sin X � Cos X � (Sin X + Cos X)^2

SOLUTION: Prove the identity: 2Sin X � Cos X � (Sin X + Cos X)^2 - 1 = 1

Question 988758: Prove the identity:
2Sin X � Cos X � (Sin X + Cos X)^2 - 1 = 1

Answer by Shai(25) (Show Source): You can put this solution on YOUR website!
Let the numerator be as it is
Now lets resolve the denominator:
(sinx + cosx)^2=sin^x+cos^x+2sinx.cosx
Since we know that according to the trigonometry
Identity sin^x+cos^x=1 hence the denominator
Becomes (1+2sinx.cosx)-1,1 and 1 cancels
And the equation becomes 2sinx.cosx/2sinx.cosx
Which is 1
Henceforth lhs=RHS
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