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Question
If sin `(sin^-1 1/5 + cos^-1 x) = 1`, then find the value of x.
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Solution
sin `(sin^-1 1/5 + cos^-1 x) = 1`
∴ `sin^-1 1/5 + cos^-1 "x" = sin^-1 (1)`
∴ `sin^-1 1/5 + cos^-1 "x" = sin^-1 (sin pi / 2)`
∴ `sin^-1 1/5 + cos^-1 "x" = pi/2`
∴ x = `1/5 .....[because sin^-1"x" + cos^-1 "x" = pi/2]`
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