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Please help!!!

Simplify: (sin 0 - cos 0)2 + (sin 0 + cos 0)2 (5 points)
Select one:
a. 1
b. 2
c. sin^2theta
d. cos^2theta

1 Answer

2 votes

Answer:

B

Explanation:

(To save time, I'm going to use x instead of θ)

So we have the expression:


(\sin(x)-\cos(x))^2+(\sin(x)+\cos(x))^2

First, expand these binomials:


=(\sin^2(x)-2\sin(x)\cos(x)+\cos^2(x))+(\sin^2(x)+2\sin(x)\cos(x)+\cos^2(x))

Combine like terms:


=\sin^2(x)+\sin^2(x)+\cos^2(x)+\cos^2(x)-2\sin(x)\cos(x)+2\sin(x)\cos(x)\\=2\sin^2(x)+2\cos^2(x)

Factor out a 2:


=2(\sin^2(x)+\cos^2(x))

The expression inside the parentheses is the Pythagorean Identity:


\sin^2(x)+\cos^2(x)=1

Substitute:


=2(1)\\=2

The answer is B.