Differentiate `tan^(-1){x/(sqrt(a^2-x^2))}\ ,\ -a

Explanation

Solution:


`y=\tan ^{-1}\{\frac{x}{a+\sqrt{a^{2}-x^{2}}}\}`

Let `x=a \sin \theta`

`y=\tan ^{-1}\{\frac{a \sin \theta}{a+\sqrt{a^{2}-a^{2} \sin ^{2} \theta}}\} `

`\sin ^{2} \theta+\cos ^{2} \theta=1`

`y=\tan ^{-1}\{\frac{a \sin \theta}{a+a \sqrt{\cos ^{2} \theta}}. `

`y=\tan ^{-1}\{\frac{\sin \theta}{1+\cos \theta}\}`

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