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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`
We know that
`sin^(−1)(1/5)+cos^(−1) x=pi/2`
Now, from equations (1) and (2), we have:
`sin^(−1)(1/5)-sin^(−1) x=0`
`sin^(−1)(1/5)=sin^(−1) x`
`x=sin(sin^(-1)(1/5))`
`x=1/5`
the value of x is `1/5`
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