Which of the following is/are true ?

Options

A. `"tan"^(-1)(1)/(3)=(1)/(2)"sin"^(-1)(3)/(5)`
B. `"tan"^(-1)(1)/(3)=(pi)/(4)-cot^(-1)2`
C. `"tan"^(-1)(1)/(3)=(pi)/(4)-(1)/(2)"cos"^(-1)(4)/(5)`
D. `"tan"^(-1)(1)/(3)=(pi)/(2)-cot^(-1)3`

Answer

A, B, C

Explanation

`"tan"^(-1)(1)/(3)+"tan"^(-1)(1)/(2)=(pi)/(4)`
`rArr "tan"^(-1)(1)/(3)=(pi)/(4)-"tan"^(-1)(1)/(2)=(pi)/(4)-cot^(-1)2`
Also `2"tan"^(-1)(1)/(3)="tan"^(-1)((2)/(3))/(1-(1)/(9))="tan"^(-1)(3)/(4)`
`= "sin"^(-1)(3)/(5)=(pi)/(2)-"cos"^(-1)(4)/(5)`