If 2f( x)+f( x)=x then f'(x)=

Correct Answer is : 11−x2{1}{{1-x²}}1−x21

Correct Answer is : 11−x2{1}{{1-x²}}1−x21

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AP EAMCET Engineering 21 Sep 2020 Shift 1 Paper

Section: Mathematics

Question : 65 of 160

Marks: +1, -0

2f(\sin x)+f(\cos x)=x

f'(x)=

Solution:

It is given that,

2 f(\sin x)+f(\cos x)=x

....(i)

by replacing

x

\;\frac{\pi}{2}-x

, we get

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

...(ii)

from Eqs. (i) and (ii), we get

3 f(\sin x)=3 x-\;\frac{\pi}{2}

\Rightarrow 3 f(x)=3 \sin^{-1} x-\;\frac{\pi}{2}(

on replacing

x

\sin^{-1} x)

Now, on differentiating both sides w.r.t.

{}' X'

, we get

3 f'(x)=3\;\frac{1}{\sqrt{1-x^{2}}} \Rightarrow f'(x)=\;\frac{1}{\sqrt{1-x^{2}}}

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