If `(sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4`, then the value of `2 tan^(2)x` is

Options

A. 3
B. 4
C. 5
D. 6

Answer

C

Explanation

`(sin^(2)x-2soc^(2)x + 1)/(sin^(2)x+2cos^(2)x-1)=4`
`rArr sin^(2)x-2 cos^(2)x+1`
`=4 sin^(2)x +8 cos^(2)x-4`
`rArr 10 cos^(2)x+3 sin^(2)x-5=0`
`rArr 10+3tan^(2)x-5(1+tan^(2)x)=0`
`rArr 2 tan^(2)x=5`
`therefore tan^(2)x=(5)/(2)`