JEE Advanced Model Paper 3 with solutions for online practice

Given 2f(sinx) + f(cosx) = x
Replace x by

x

2

- x
⇒ 2f(cos) + f(sinx) =

π

2

- x
Eliminating f (cos x) from (1) and (2), we get
⇒ 3f(sinx) = 3x -

π

2

⇒ f(sinx) = x -

π

6

⇒ f(x) = sin−1x -

π

6

f(x) has the domain [-1, 1]
Also sin−1x ∊ [−

π

2.

π

2

] sin−1x -

π

6

∊ [−

2π

3

,

π

3

]