Question #c1e7d

1 Answer
Dec 13, 2016

Please see the explanation

Explanation:

Verify: (sin(θ)+cos(θ))2=1+2sin(θ)cos(θ)

I will only make changes to the left side.

Expand the square:

sin2(θ)+2sin(θ)cos(θ)+cos2(θ)=1+2sin(θ)cos(θ)

Move the swap the second and third terms:

sin2(θ)+cos2(θ)+2sin(θ)cos(θ)=1+2sin(θ)cos(θ)

Use the identity 1=sin2(θ)+cos2(θ):

1+2sin(θ)cos(θ)=1+2sin(θ)cos(θ)

Verified.