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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
The differential coefficient of the given function ${\log _e}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right)$ with respect to  $x $ is
  • A
    $cosec\,x$
  • B
    $\tan x$
  • C
    $\cos x$
  • ✓
    $\sec x$
✓

Answer

Correct option: D.
$\sec x$
d
(d) $\frac{{dy}}{{dx}} = \frac{1}{{\left( {\frac{{1 + \sin x}}{{\cos x}}} \right)}}\left[ {\frac{{\cos x\cos x + (1 + \sin x)\sin x}}{{{{(\cos x)}^2}}}} \right]$

$ = \left( {\frac{{\cos x}}{{1 + \sin x}}} \right)\frac{{{{\cos }^2}x + {{\sin }^2}x + \sin x}}{{{{(\cos x)}^2}}} = \sec x$.

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