What is the value of `"sin"^(-1)(4)/(5) + 2 "tan"^(-1)(1)/(3)` ?

Options

A. `(pi)/(3)`
B. `(pi)/(2)`
C. `(pi)/(4)`
D. `(pi)/(6)`

Answer

B

Explanation

Consider `"sin"^(-1)(4)/(5)+"2 tan"^(-1)(1)/(3)`
`=tan^(-1)((4//5)/(sqrt(1-16//25)))+tan^(-1)((2//3)/(1-1//9))" "[because sin^(-1)x="tan"^(-1)(x)/(sqrt(1-x^(2)))and 2 tan^(-1)x=tan^(-1)((2x)/(1-x^(2)))]`
`=tan^(-1)((4//5)/(3//5))+tan^(-1)((2//3)/(8//9))`
`=tan^(-1)((4)/(3))+ tan^(-1)((3)/(4))`
`=tan^(-1)((4)/(3))+cot^(-1)((4)/(3))=(pi)/(2)" "(because tan^(-1)x + cot^(-1)x=(pi)/(2))`