If `5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9`, then the value of `cos 4 x ` is

Options

A. `2/9`
B. `7/9`
C. `3/5`
D. `1/3`

Answer

B

Explanation

We have,
`5(tan^(2)x-cos^(2)x)=2cos2x+9`
`implies5{(1-cos2x)/(1+cos2x)-(1+cos2x)/(2)}=2cos2x+9`
`implies5((1-t)/(1+t)-(1+t)/(2))=2t+9, where t =cos2x`
`implies9t^(2)+72t+13=0`
`implies(3t+1)(3t+13)=0implies3t+1=0" "[because-1let le1]`
`impliest=1/3impliescos2x =-1/3`
Hence, `cos4x=2cos^(2)2x-12/9-1=7/9`