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  • Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): sin x + cos x / sin x - cos x

17.  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): \frac{\sin x + \cos x }{\sin x - \cos x }

Answers (1)

best_answer

Given 

f(x)=\frac{\sin x + \cos x }{\sin x - \cos x }

Also can be written as

f(x)=\frac{\tan x + 1 }{\tan x - 1 }

which further can be written as

f(x)=-\frac{\tan x + tan(\pi/4) }{1-\tan(\pi/4)\tan x }

f(x)=-\tan(x-\pi/4)

Now,

f'(x)=-\sec^2(x-\pi/4)

f'(x)=-\frac{1}{\cos^2(x-\pi/4)}

Posted by

Pankaj Sanodiya

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