The equation sin^-1 x-cos^-1 x=(π)/6 has

Correct answer: (B) unique solution. sin^-1 x-cos^-1 x=(π)/6 … (i) We know that, sin^-1 x+cos^-1 x=(π)/2 … (ii) On adding, sin^-1 x=(π)/3

Q171 / 270 · NDA 2021 (Phase 1) · Mathematics

The equation $\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6}$ has

A
no solution
Correct answer
B
unique solution
C
two solutions
D
infinite number of solutions

Solution

$\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6} \ldots$ (i) We know that, $\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2} \ldots$ (ii) On adding, $\sin ^{-1} x=\frac{\pi}{3}$

Hence, the correct answer is option: 'B'.

The equation $\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6}$ has

Solution

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