Question
Question: If f(x) = sin<sup>–1</sup> (sin x) + cos<sup>–1</sup> (sin x) and φ(x) = f(f(f(x))), then φ′(x) –...
If f(x) = sin–1 (sin x) + cos–1 (sin x) and φ(x) = f(f(f(x))),
then φ′(x) –
A
1
B
sin x
C
0
D
None of these
Answer
0
Explanation
Solution
sin–1(x) + cos–1(x) = π/2
∴ f(x) = π/2 (a constant function)
⇒ φ′(x) = 0.