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Question
Solve:
sin–1 (x) + sin–1 (1 – x) = cos–1 x
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Solution
sin–1 (x) + sin–1 (1 – x) = cos–1 x
⇒ `sin^-1(x) + sin^-1(1 - x) = π/2 - sin^-1x`
⇒ `sin^-1(1 - x) = π/2 - 2sin^-1x`
⇒ `(1 - x) = sin(π/2 - 2sin^-1x)`
⇒ (1 – x) = cos (2 sin–1 x)
⇒ (1 – x) = cos (cos–1 (1 – 2x2))
⇒ (1 – x) = 1 – 2x2
⇒ 2x2 – x = 0
∴ x = `0, 1/2`
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