Complete the identity (sinx+cosx)^2/1+2sinxcosx=?
A. 1-sinx
B. -sec^2x
C. 0
D. 1
To simplify the given expression, we need to expand (sinx+cosx)^2 and then apply the Pythagorean identity sin^2(x)+cos^2(x)=1.
(sin(x)+cos(x))^2 = sin^2(x) + 2sin(x)cos(x) + cos^2(x)
Now, replace sin^2(x) + cos^2(x) with 1:
= 1 + 2sin(x)cos(x)
So, the given expression becomes:
(1 + 2sin(x)cos(x))/(1 + 2sin(x)cos(x))
= 1
Therefore, the correct answer is:
D. 1