If f(x) `=cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))}` then `f(2/3)` equalsA. `(pi)/(3)`B. `2 cos^(-1) 2/3 -(pi)/(3)`C. `(2pi)/(3)`D. `2cso^(-1)2/3`

If f(x) `=cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))}` then `f(2/3)` e

1.	If f(x) `=cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))}` then `f(2/3)` equalsA. `(pi)/(3)`B. `2 cos^(-1) 2/3 -(pi)/(3)`C. `(2pi)/(3)`D. `2cso^(-1)2/3`
Answer» We have `cos^(-1){xy+sqrt(1-x^(2))sqrt(1-y^(2))}` `={:(cos^(-1)x-cosf^(-1)y, if -1 le x,y le 1 and x le y),(cos^(-1)y-cos^(-1)x if -1 le y le 0, 0 le x le 1 and y le x):}` ` rarr f(2/3)= cos^(-1)1/2=(pi)/(3)`

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