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The number of solutions of the equation $2 \sin^{- 1} \sqrt{x^{2} - x + 1} + \cos^{- 1} (\sqrt{x^{2} - x}) = \frac{3 π}{2}$ is

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a

0

b

infinite

c

2

d

4

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detailed solution

Correct option is C

sin–1x, cos–1x are defined for x ≤ 1 and x ≥ 0∴x2−x+1<1 and x2−x>0⇒x2−x≤0 and x2−x≥0⇒x2−x=0⇒x=1,0∴ There are two solutions, both satisfy the equation.

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