If cos^(-1) sqrtp + cos^(-1) sqrt(1 -p) ...

If `cos^(-1) sqrtp + cos^(-1) sqrt(1 -p) + cos^(-1) sqrt(1 - q) = (3pi)/(4)`, then the value of `q` is

A

`(1)/sqrt(2)`

B

1

C

`1/2`

D

`1/3`

Text Solution

Verified by Experts

Clearly left hand side of the given equation is meaning if `0 le p le 1 and 0 le q le 1`
Let `p cos^(2) theta` Then
`cos^(-1)sqrt(p)+cos^(-1)sqrt(1-p) + cos^(-1) sqrt(1-q)=(3pi)/(4)`
`rarr cos ^(-1)(cos theta) + cos^(-1)(sin theta)+cos^(-1)sqrt(1-q)=(3pi)/(4)`
`rarr cos^(-1)sqrt(1-q)=(pi)/(4)`
`rarr sqrt(1-q)=(1)/sqrt(2) rarr 1- q=1/2 rarr =1/2`

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