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The set of lines x tan^(- 1)a+ysin^(- 1)...

The set of lines `x tan^(- 1)a+ysin^(- 1)(1/(sqrt(1+a^2)))+2=0` where ` ain (0,1) ` are concurrent at (a) `(1/pi,1/pi)` (b) `(-4/pi,-4/pi)` (c) `(pi,pi)` (d) none of these

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The correct Answer is:
B
Since `a in (0,1)`
`rArr "sin"^(-1) (1)/(sqrt(1+a^(2))) = "cot"^(-1)a=(pi)/(2)-"tan"^(-1)a`
`"Now, "x"tan"^(-1) a+y"sin"^(-1)(1)/(sqrt(1+a^(2))) + 2 =0`
`rArr x"tan"^(-1)a+y((pi)/(2)-"tan"^(-1)a)+2=0`
`rArr (x-y)"tan"^(-1)a+((piy)/(2)+2)=0`
Clearly, this passes through `(-(4)/(pi), -(4)/(pi))`.
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