Find derivative of trigonometric function y=(3(1-sin x))/(2cos x)

Question

Find derivative of trigonometric function

y = \frac{3 (1 - \sin x)}{2 \cos x}

Answer 1

Simplify the trigonometric function

y = \frac{3 (1 - \sin x)}{2 \cos x}

y = \frac{3}{2} (\frac{1}{\cos x} - (\frac{\sin x}{\cos x}))

y = \frac{3}{2} (\sec x - \tan x) {∵ \frac{1}{\cos x} = \sec x and \frac{\sin x}{\cos x} = \tan x}

Derivative of trigonometric function:

y = \frac{3}{2} (\sec x - \tan x)

\frac{d y}{d x} = \frac{d}{d x} (\frac{3}{2} (\sec x - \tan x))

\frac{d y}{d x} = \frac{3}{2} (\frac{d}{d x} (\sec x) - \frac{d}{d x} (\tan x))

\frac{d y}{d x} = \frac{3}{2} ((\sec x \cdot \tan x) - \sec^{2} x) {∵ \frac{x}{d x} (\sec x) = (\sec x \cdot \tan x) and d (d x) (\tan x) = \sec^{2} x}

The derivative of function is given below

\frac{d y}{d x} = \frac{3}{2} ((\sec x \cdot \tan x) - \sec^{2} x)

Answer 2

Jeffrey Jordon

Answered 2021-12-14 Author has 2064 answers

Answer is given below (on video)

Expert Answer