If sin x


If $\sin x=\frac{12}{13}$ and $x$ lies in the second quadrant, find the value of $\sec x+\tan x$.


We have:

$\sin x=\frac{12}{13}$ and $x$ lie in the second quadrant.

In the second quadrant, $\sin x$ and $\operatorname{cosec} x$ are positive and all the other four $\mathrm{T}-$ ratios are negative.

$\therefore \cos x=-\sqrt{1-\sin ^{2} x}$



$\tan x=\frac{\sin x}{\cos x}$



And, $\sec x=\frac{1}{\cos x}$



$\therefore \sec x+\tan x=\frac{-13}{5}+\frac{-12}{5}$



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