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. 1C. `1/2`D. `1/3`

if `cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4` ,t

1.	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. 1C. `1/2`D. `1/3`
Answer» 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`

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
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