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