Question

Solve the equation `sin^(4)x + cos^(4)x =7/2 sinx.cosx.`

Answer 1

`sin^(4)x+cos^(4)x=7/2sinx.cosx rArr (sin^(2)x +cos^(2)x)^(2) =7/2sinx.cosx`
`rArr 1-1/2(sin2x)^(2)=7/4(sin2x) rArr 2sin^(2)2x+7sin2x-4=0`
`rArr (2sin2x-1)(sin2x+4) =0 rArr sin2x =1/2` or `sin2x = -4` (Which is not possible) `rArr 2x = npi+(-1)^(n)pi/6 , n in I`
i.e, `x=(npi)/(2)+(-1)^(n)pi/12, n in I` Ans.