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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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