Trigonometry

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use the double angle formula to rewrite.

6cos^2-3

and


(cosx +sinx)(cosx-sinx)

  • Trigonometry -

    cos ( 2 x ) = 2 cos ^ 2 ( x ) - 1


    6 cos ^ 2 ( x ) - 3 =

    3 [ 2 cos ^ 2 ( x ) - 1 ] =

    3 sin ( 2 x )

  • Trigonometry -

    second one:

    (cosx +sinx)(cosx-sinx)
    =(cosx +sinx)(cosx-sinx) * (cosx + sinx)/(cosx + sinx)
    = (cos^2 x + 2sinxcosx + sin^2 x)/(cos^2 x - sin^2 x)
    = (1 + sin 2x)/cos 2x
    or
    1/cos 2x + sin 2x/cos 2x
    = sec 2x + tan 2x

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