The general solution of `4 sin^4 x + cos^4x= 1` is

Options

A. `n pi pm alpha//2, alpha=cos^(-1) (1//5), AA n in Z`
B. `n pi pm alpha//2, alpha=cos^(-1) (3//5), AA n in Z`
C. `2 n pi pm alpha//2, alpha=cos^(-1) (1//3), AA n in Z`
D. none of these

Answer

A

Explanation

`4 sin^(4) x+cos^(4) x=1`
`rArr (2 sin^(2) x)^(2) +1/4 (2 cos^(2) x)^(2)=1`
or `(1-cos 2x)^(2) +1/4 (1+ cos 2x)^(2)=1`
or `5 cos^(2) 2x-6 cos 2x+1=0`
or `(cos 2x-1)(5 cos 2x-1)=0`
or `cos 2x=1 or cos 2x=1/5`
`rArr 2x=2npi or 2x=2npi pm alpha`,
where `alpha=cos^(-1) (1/5), AA n in Z`