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Question Number 145208 by imjagoll last updated on 03/Jul/21

$$\mathrm{If}\mathrm{P}:\mathrm{Q}=\tan 2\mathrm{A}:\cos \mathrm{A}$$$$\mathrm{Q}:\mathrm{R}=\cos 2\mathrm{A}:\sin 2\mathrm{A}$$$$\mathrm{then}\mathrm{P}:\mathrm{R}=?$$

Answered by EDWIN88 last updated on 03/Jul/21

$$\frac{P}{Q}=\frac{2\sin A\cos A}{\cos 2A\cos A}=\frac{2\sin A}{\cos 2A}$$$$P=\frac{2\sin AQ}{\cos 2A}...\left(i\right)$$$$\frac{Q}{R}=\frac{\cos 2A}{\sin 2A}\Rightarrow R=\frac{\sin 2AQ}{\cos 2A}...\left(ii\right)$$$$thus\frac{P}{R}=\frac{2\sin AQ}{\cos 2A}.\frac{\cos 2A}{\sin 2AQ}$$$$=\frac{2\sin A}{2\sin A\cos A}=\frac{1}{\cos A}$$

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