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If sin (sin^(−1)(1/5)+cos^(−1) x)=1, then find the value of x. - Mathematics

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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`

 

 

Concept: Properties of Inverse Trigonometric Functions
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