Exams › SSC CGL (Prelims) › General

If $\sin^2\theta-\cos^2\theta=-\frac{1}{3}$, find the value of $\cos^2\theta$.

1. $1/3$
2. $1/2$
3. $2/3$
4. $5/6$

Correct answer: $2/3$

Solution

Using $\sin^2\theta=1-\cos^2\theta$, we get $(1-\cos^2\theta)-\cos^2\theta=-\frac13$. This gives $1-2\cos^2\theta=-\frac13$, so $\cos^2\theta=\frac23$.

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