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Data processing in precise time and frequency applications

admin 26/05/2021

`L.H.S. = 2(sin^6x+cos^6x) - 3(sin^4x+cos^4x) +1``= 2((sin^2x)^3+(cos^2x)^3) - 3((sin^2x)^2+(cos^2x)^2) +1`As, `a^3+b^3 = (a+b)^3-3ab(a+b) & a^2+b^2 = (a+b)^2-2ab`,So, it becomes,`= 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``=2-6sin^2xcos^2x-3+6sin^2xcos^2x+1``=0 = R.H.S.`

` " title="Prove sầu that `(cos 3 x)/(sin 2 xsin 4x)+(cos 5x)/(sin 4xsin 6x)+(cos 7x)/(sin 6xsin 8x)+(cos 9x)/(sin 8x sin 10x)` `=(1)/(2) (teo sec x)` " style="width:100%;height:;"/>

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Data processing in precise time and frequency applications

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