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if cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+c...

if `cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4` ,then the value of q is (A) 1 (B) `1/sqrt(2)` (C) `1/3` (D) `1/2`

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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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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