MCQ
જો $2f(sinx) + f(cos x) = x,$ તો $\frac{d}{{dx}}$ $f(x)$ મેળવો.
- A$sinx + cosx$
- B$2$
- ✓$\frac{1}{{\sqrt {1 - {x^2}} }}$
- Dએકપણ નહીં.
$x \rightarrow \frac{\pi}{2}-x$
$2 f(\cos x)+f(\sin x)=\frac{\pi}{2}-x$
$4 f(\cos x)+2 f(\sin x)=\pi-2 x$ .........$(2)$
$(1)-(2)$
$-3 f(\cos x)=3 x-\pi$
$f(\cos x)=\frac{\pi}{3}-x$
$f(x)=\frac{\pi}{3}-\cos ^{-1} x$
$f^{\prime}(x)=\frac{1}{\sqrt{1-x^{2}}}$
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