Question

Find derivative of the following:-​

Answer 1

Answer:

dy/dx = 1 / 2

Step-by-step explanation:

Given--->

y = tan⁻¹ { ( 1 + Sinx ) / Cosx }

To find---> Derivative of given function

Solution--->

1) Plzzz refer to the attachment

2) In 2nd step we apply three formlee of trigonometery

a) Sin²θ + Cos²θ = 1

b) Sinθ = 2 Sin θ / 2 Cos θ / 2

c) Cosθ = Cos²θ/2 - Sin²θ/2

3) In 3rd step we have two identity

a) ( a + b )² = a² + b² + 2ab

b) a² - b² = ( a + b ) ( a - b )

Applying these properties in 3rd and 4th step respectively.

4) Then dividing each term of numerator and denominator by Cosx/2 and applying a formula

tanθ = Sinθ / Cosθ

5) Now putting , 1 = tanπ/4 , in 8th step

6) Now we have a formula,

tan ( x + y ) =( tanx + tany ) / ( 1 - tanx tany )

Applying it in 9th step

7) Now differentiating with respect to x and applying a formula

d / dx ( x ) = 1

Answer 2

I hope this helps you.

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