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Show that 2(sin^6x+cos^6x)-3(sin^4x+cos^...

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

Text Solution

Verified by Experts

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

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

Knowledge Check

  • int (sin^6x+cos^6x+3 sin^2x cos^2 x)dx is equal to

    A
    x+c
    B
    `3/2 "sin"2x+C`
    C
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    D
    `1/3"sin"3x-cos 3x+C`

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