Differentiation Question 240
Question: The differential coefficient of the given function $ {\log _{e}}( \sqrt{\frac{1+\sin x}{1-\sin x}} ) $ with respect to x is
[MP PET 1993]
Options:
A) $ \cos ecx $
B) $ \tan x $
C) $ \cos x $
D) $ \sec x $
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Answer:
Correct Answer: D
Solution:
$ \frac{dy}{dx}=\frac{1}{( \frac{1+\sin x}{\cos x} )}[ \frac{\cos x\cos x+(1+\sin x)\sin x}{{{(\cos x)}^{2}}} ] $
$ =( \frac{\cos x}{1+\sin x} )\frac{{{\cos }^{2}}x+{{\sin }^{2}}x+\sin x}{{{(\cos x)}^{2}}}=\sec x $ .
BETA
