सिद्ध कीजिए कि -
` sin ^(8) theta - cos^(8) theta = ( sin^(2) theta - cos^(2) theta ) ( 1 - 2 sin^(2) theta cos^(2) theta )`

Explanation

` L.H.S = sin^(8) theta - cos^(8) theta`
` = (sin^(4) theta)^(2)- ( cos^(4) theta)^(2)`
` = ( sin^(4) theta - cos^(4) theta) ( sin^(4) theta + cos^(4) theta)`
` = [ ( sin^(2) theta)^(2) - (cos^(2)theta)^(2)]`
` [ (sin^(2) theta)^(2) + ( cos^(2) theta)^(2)`
` + 2 sin^(2) theta cos^(2) theta - 2 sin^(2) theta cos^(2) theta]`
` = ( sin^(2) theta + cos^(2) theta) (sin^(2) theta - cos^(2) theta) `
` [ ( sin^(2) theta + cos^(2) theta)^(2) - 2 sin^(2) theta cos^(2) theta]`
` = 1* ( sin^(2) theta - cos^(2) theta) (1^(2) - 2sin^(2) theta cos^(2) theta)`
` = (sin^(2) theta - cos^(2) theta) ( 1-2 sin^(2) thetacos^(2) theta)`
` = R.H.S`