1.

Show that `2(sin^6x+cos^6x)-3(sin^4x+cos^4x)+1=0`.

Answer» `2(sin^6x+cos^6x)-3(sin^4x+cos^4x)+1`
`=2[(sin^2x)^3+(cos^2x)^(3)]-3(sin^4x+cos^4x)+1`
`=2[(sin^2x+cos^2x)^3-3sin^2xcos^2x(sin^2x+cos^2x)]-3[(sin^2x+cos^2x)^2-2sin^2xcos^2x]+1`
`=2[1-3sin^2xcos^2x]-3[1-2sin^2xcos^2x]+1=0`


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