Question 54

If $$\cos \theta = \frac{2p}{p^2 + 1}$$, then $$\sin \theta$$ is equal to:

Solution

$$\cos \theta = \frac{2p}{p^2 + 1}$$

We know , $$\cos^2 \theta$$ + $$\sin^2 \theta $$= 1

Hence ,

$$\sin^2 \theta = $$1 -$$\left(\frac{2p}{p^2 + 1}\right)^2$$

$$\sin\ ^2\theta\ =\ \frac{\left(p^2+1-2p\right)}{\left(p^2+1\right)^2}$$

$$\sin\ ^2\theta\ =\ \frac{\left(p^2-1\right)^2}{\left(p^2+1\right)^2}$$

$$\sin\ ^2\theta\ =\ \frac{p^2-1}{p^2+1}$$

Hence , option C is correct.

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