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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $2f(sinx) + f(cos x) = x,$ then $\frac{d}{{dx}}$ $f(x)$ is
  • A
    $sinx + cosx$
  • B
    $2$
  • ✓
    $\frac{1}{{\sqrt {1 - {x^2}} }}$
  • D
    None of these
✓

Answer

Correct option: C.
$\frac{1}{{\sqrt {1 - {x^2}} }}$
c
$2 f(\sin x)+f(\cos x)=x$          ........$(1)$

$x \rightarrow \frac{\pi}{2}-x$

$2 f(\cos x)+f(\sin x)=\frac{\pi}{2}-x$

$4 f(\cos x)+2 f(\sin x)=\pi-2 x$              .........$(2)$

$(1)-(2)$

$-3 f(\cos x)=3 x-\pi$

$f(\cos x)=\frac{\pi}{3}-x$

$f(x)=\frac{\pi}{3}-\cos ^{-1} x$

$f^{\prime}(x)=\frac{1}{\sqrt{1-x^{2}}}$

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