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The total number of solution of the equa...

The total number of solution of the equation `sin^4 x +cos^4 x = sin x cos x` in `[0,2pi]` is :

Text Solution

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`(sin^2x+cos^2x)-2sin^2xcos^2x=sinxcosx`
`sina*cosx=t`
`1-2t^2=t`
`2t^2+t-1=0`
`2t^2-t+2t-1=0`
`(t+1)(2t-1)=0`
`t=-1,1/2`
`t=(2sinxcosx)/2=sin(2x)/2`
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