sin^1/2x cos x – sin^5/2x cosx = cos^3x sqrt sinx?

verify the identity?

3 Answers

  • sin^1/2x cos x – sin^5/2x cosx = sin^(1/2)x (cos x – sin^2 x cos x)

    = sqrt(sin x) (cos x) (1 – sin^2 x) = sqrt(sin x)(cos x)(cos^2 x)

    = cos^3 x * sqrt(sin x)

  • cos x (sin x)^1/2 – cos x (sin x)^(5/2)

    = cos x sin(x)^1/2 [ 1 – sin^2(x) ]

    = cos x sin(x)^1/2 [ cos^2(x) ]

    = cos^3(x) √(sin x)

  • sin^1/2xcosx(1-sin^2x)

    =sin^1/2xcosx(cos^2x)

    = cos^3xsin^1/2x

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