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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
Given:
`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) pi/2`
`=> sin^-1 (1/5) = -cos^-1 x`
`=> sin^-1 (1/5) = sin^-1 x`
`(sin^-1x + cos^-1 x = pi/2)`
`x = 1/5`
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