The value of `cos[2tan^(-1)(-7)]` is

Options

A. `(49)/(50)`
B. `-(49)/(50)`
C. `(24)/(25)`
D. `-(24)/(25)`

Answer

D

Explanation

`cos[2tan^(-1)(-7)]=cos[cos^(-1)((1-49)/(1+49))]`
`[because2tan^(-1)x=cos^(-1)((1-x^(2))/(1+x^(2)))]`
`=cos[pi-cos^(-1)((48)/(50))]=-cos{cos^(-1)((48)/(50))}=-(24)/(25)`