Question

If $p\left[\frac{2\sin 30^\circ}{1 - \sin^2 30^\circ}\right] = q\left[\frac{2\sin 30^\circ}{1 + \sin^2 30^\circ}\right]$, then $p : q$ is equal to:

Accepted Answer

C. Substitute $\sin 30^\circ = \frac{1}{2}$: $$p\left[\frac{2(1/2)}{1 - 1/4}\right] = q\left[\frac{2(1/2)}{1 + 1/4}\right]$$ $$p\left[\frac{1}{3/4}\right] = q\left[\frac{1}{5/4}\right]$$ $$p \cdot \frac{4}{3} = q \cdot \frac{4}{5} \implies \frac{p}{q} = \frac{3}{5}$$

Trigonometric identities and ratio

Explanation

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