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1) Use double-angle identities to write the following expression, using trigonometric functions of x instead of 4x.
cos 4x


2) Use half-angle identities to write the following expression, using trigonometric functions of x instead of x/4.

sin x/4

  • trig -

    cos4x = 2cos^2(2x)-1
    = 2(2cos^2(x)-1)^2 - 1
    just expand that

    sin(x/4) = sqrt((1-cos(x/2))/2)
    = sqrt((1-sqrt((1-cos(x))/2)/2

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