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Q.

The number of solutions of the equation $\sin \sin^{- 1} ([x]) + \cos^{- 1} \cos x = 1$ where [.] denote the greatest integer function, is

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a

One

b

Three

c

Zero

d

Two

answer is D.

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Detailed Solution

Domain of LHS is [-1, 2)

$- 1 \leq x < 0, - 1 - x = 1 \Rightarrow x = - 2$

For $\begin{matrix} 0 \leq x < 1, 0 + x = 1 \Rightarrow x = 1 \\ 1 \leq x < 2, 1 + x = 1 \to x = 0 \end{matrix}$

$∴$ no solution

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