If f(x) = s i n − 1 ( s i n x ) + c o s − 1 ( s i n x ) a n d ϕ ( x ) = f ( f ( f ( x ) ) ) , t h e n ϕ ′ ( x ) is equal to Options: A . &nbsp1 B . &nbspsin x C . &nbsp0 D . &nbspNone of these

Answer: Option C : C f ( x ) = π 2 ( a c o n s t a n t f u n c t i o n ) ⇒ ϕ ′ ( x ) = 0

If f(x) = sin−1(sin x)+cos−1(sin x) and ϕ

Question

If f(x) =

s i n^{- 1} (s i n x) + c o s^{- 1} (s i n x) a n d ϕ (x) = f (f (f (x))), t h e n ϕ^{'} (x)

is equal to

Options:

A . 1

B . sin x

C . 0

D . None of these

Answer: Option C
:
C

f (x) = \frac{π}{2} (a c o n s t a n t f u n c t i o n)

\Rightarrow ϕ^{'} (x) = 0

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