If $\sec x+ an x=3, x \in\left(0, \frac{\pi}{2} ight)$ then, $\sin x=$

Question

If $\sec x+	an x=3, x \in\left(0, \frac{\pi}{2}ight)$ then, $\sin x=$

Aicharya · Accepted Answer

We have $\sec x+	an x=3$ ...(1) We know that $\sec ^{2} x-	an ^{2} x=1$ $	herefore(\sec x-	an x)(\sec x+	an x)=1 \Rightarrow \sec x-	an x=\frac{1}{3}$ ...(2) Adding (1) and (2) $2 \sec x=\frac{10}{3} \Rightarrow \sec x=\frac{5}{3} \Rightarrow \cos x=\frac{3}{5} \Rightarrow \sin x=\sqrt{1-\cos ^{2} x}=\frac{4}{5}$

If $\sec x+\tan x=3, x \in\left(0, \frac{\pi}{2}\right)$ then, $\sin x=$

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