solve this Q y = tan-11+sin x+1-sin x1+sin x-1-sin x find dydx - Maths - Continuity and Differentiability

Question

solve this
Q y = tan - 1 1 + sin   x + 1 - sin   x 1 + sin   x
- 1 - sin   x find d y d x

Koka Sri Lakshmi Divya Sai · Accepted Answer

Giveny=tan-11+sinx+1-sinx1+sinx-1-sinx⇒y=tan-11+sinx+1-sinx1+sinx-1-sinx×1+sinx+1-sinx1+sinx+1-sinx⇒y=tan-11+sinx+1-sinx+21-sin2x1+sinx-1+sinx⇒y=tan-12+2cos2x2sinx⇒y=tan-12+2cosx2sinx⇒y=tan-11+cosxsinx⇒y=tan-12cos2x22sinx2cosx2⇒y=tan-1cosx2sinx2⇒y=tan-1cotx2⇒y=tan-1tanπ2-x2⇒y=π2-x2⇒dydx=0-12⇒dydx=-12

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solve this Q. y = tan - 1 1 + sin x + 1 - sin x 1 + sin x - 1 - sin x find d y d x .

solve this
Q. y = $\tan^{- 1} \{\frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}}\}$ find $\frac{d y}{d x}$ .