Answer to Question #121892 in Calculus for desmond

Question

it is given that f(x)=tan^-1 2x and g(x) =p tan^-1 x, where p is a contant. find the value of p for which f(1/2)=g(1/2)

Answer 1

f(x) = tan^-12x and g(x) = p tan^-1x

Given that f($\frac {1}{2}$ ) = g($\frac {1}{2}$ )

=> tan^-1(2*$\frac {1}{2}$ ) = p tan^-.1 ($\frac {1}{2}$ )

=> tan^-11 = p cot^-12

So p cot^-12 = tan^-11

=> p cot^-12 = $\frac {π}{4}$

=> p = $\frac {π}{4cot^{-1}2}$

So value of p is $\frac {π}{4cot^{-1}2}$ which is approximately 1.69395