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Question
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Options
`0, 1/2`
`1, 1/2`
0
`1/2`
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Solution
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to 0.
Explanation:
sin–1 (1 – x) – 2 sin–1 x = `pi/2`
⇒ sin–1 (1 – x) = `pi/2 + 2 sin^-1 x`
⇒ 1 − x = cos[cos−1 (1 − 2x2)]
⇒ 1 − x = 1 − 2x2
⇒ 2x2 − x = 0
⇒ x = `0, 1/2`
But x = `1/2` does not satisfy the equation, so x = 0.
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