Question

$\sf Differentiate \: the \:following \:function \:w.r.t \: x$


$\sf {tan}^{-1} (\frac { \sqrt { 1 + sin x } + \sqrt {1 - sinx }}{\sqrt{ 1 + sinx } - \sqrt { 1 - sinx }})$



$\sf The\:answer\:is\: \frac {1}{2}$




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Answer 1

Answer:

- 1 / 2

Step-by-step explanation:

Given----->

tan⁻¹ { √1 + Sinx + √1 - Sinx /√1 + Sinx - √1 - Sinx }

To find ---> Derivative of given function

Solution----> 1) Plzz see the attachement

2) In second step we multiply in numerator and denominator by the conjugate of denominator and using identities ,

( a + b )² = a² + b² + 2ab , in numerator and

( a - b ) ( a + b ) = ( a² - b² ) , in denominator ,

3) In 8th step we use

1 - Sin²θ = Cos²θ

4) In 11th step we use ,

CosA = 2 Cos²A/2 - 1

SinA = 2 SinA/2 CosA/2

5) In 14th step we use

Cosθ / Sinθ = Cotθ

6) In 15th step we use ,

Cotθ = tan ( π/2 - θ )

and we get,

y = π/2 - x / 2

Differentiating with respect to x , we get,

dy/dx = 0 - 1/2

= - 1/2

Answer 2

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