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Simplify: (sin θ − cos θ) − (sin θ + cos θ)2 (5 points)

Simplify: (sin θ − cos θ) − (sin θ + cos θ)2 (5 points)-example-1

1 Answer

2 votes
I'll use x instead of theta

(sin(x) - cos(x)) - (sin(x) + cos(x))^2
(sin(x) - cos(x)) - (sin^2(x) + 2*sin(x)*cos(x) + cos^2(x))
(sin(x) - cos(x)) - (sin^2(x) + cos^2(x) + 2*sin(x)*cos(x))
(sin(x) - cos(x)) - (1 + 2*sin(x)*cos(x))
sin(x) - cos(x) - 1 - 2*sin(x)*cos(x)
- 2*sin(x)*cos(x) - cos(x) + sin(x) - 1

The final answer is choice D



User Marcus Edensky
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