\(\rm \sec \left(\tan^{-1}\dfrac{y}{2}\right)\) चे मूल्य किती आहे?

Question

Question

Answer 1

संकल्पना:

गणना:

असे म्हणूया की \(\rm \tan^{-1}\dfrac{y}{2}=\theta\), जिथे =\(\rm \theta \in \left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]\).

\(\rm \Rightarrow \tan \theta = \dfrac{y}{2}\)

\(\rm \Rightarrow \tan^2 \theta = \dfrac{y^2}{4}\)

\(\rm \Rightarrow 1+\tan^2 \theta = 1+\dfrac{y^2}{4}=\dfrac{y^2+4}{4}\)

\(\rm \Rightarrow \sec^2 \theta = \dfrac{y^2+4}{4}\)

\(\rm \Rightarrow \sec \theta = \dfrac{\sqrt{y^2+4}}{2}\)

\(\rm \Rightarrow \sec \left(\tan^{-1}\dfrac{y}{2}\right) = \dfrac{\sqrt{y^2+4}}{2}\).