AP EAMCET Engineering 21 Sep 2020 Shift 1 Paper

It is given that,
2f(sin‌x)+f(cos‌x)=x ....(i)
by replacing x by ‌

π

2

−x, we get
2f(cos‌x)+f(sin‌x)=‌

π

2

−x...(ii)
from Eqs. (i) and (ii), we get
3f(sin‌x)=3x−‌

π

2

⇒3f(x)=3sin−1x−‌

π

2

( on replacing x by sin−1x)
Now, on differentiating both sides w.r.t. ‌′X′, we get