If sin²θ − cos²θ = −1/3, find the value of cos²θ.

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Accepted Answer

1. Use the identity: $\sin^2	heta-\cos^2	heta=-\cos2	heta$.
2. Given $\sin^2	heta-\cos^2	heta=-	frac{1}{3}$, so $-\cos2	heta=-	frac{1}{3}$ and $\cos2	heta=	frac{1}{3}$.
3. Use $\cos2	heta=2\cos^2	heta-1$. Set $2\cos^2	heta-1=	frac{1}{3}$.
4. Solve: $2\cos^2	heta=	frac{4}{3}$, so $\cos^2	heta=	frac{2}{3}$.
FINAL_ANSWER: c

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