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  • <img alt="f(x)=\frac{\tan x+\sec x-1}{\tan x-\sec x+1} \text { then } f^{\prime}(x) \text { is equal to }" src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%3D%5Cfrac%7B%5Ctan%20x&p

f(x)=\frac{\tan x+\sec x-1}{\tan x-\sec x+1} \text { then } f^{\prime}(x) \text { is equal to }

Option: 1

sec x(tanx – secx)


Option: 2

sec x(secx – tanx)


Option: 3

sec x(tanx + secx)


Option: 4

none of these


Answers (1)

best_answer

\begin{aligned} & f(x)=\left(\frac{\tan x+\sec x-1}{\tan x-\sec x+1}\right) \times\left(\frac{\tan x+\sec x+1}{\tan x+\sec x+1}\right) \\ & =\frac{\tan ^2 x+\sec ^2 x+2 \tan x \sec x-1}{(1+\tan x)^2-\sec ^2 x}=\tan x+\sec x \end{aligned}

Thus f’(x) = sec2x + secx tanx = secx (secx + tanx)

Hence (C) is correct answer.

 

Posted by

Rishabh

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