trig

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transform the expression on left to one on right
csc x-sin x to cot x cos x

  • trig -

    csc x-sin x = (1/sinx) - sin x
    = (1 - sin^2 x)/sin x = (cos x * cos x)/sin x
    = cos x cot x

  • trig -

    We have trig identities.

    cscx - sinx to cotx(cos x).

    cscx is the reciprocal of the sine function.

    So, then:

    cscx = 1/sinx

    We now have:

    1/sinx - sinx...Treat this like a fraction case.

    1/sinx - sinx becomes (1 - sin^2x)/sinx

    Of course, (1 - sin^2x) is one of the Pythagorean Identities, recall?

    We know that (1 - sin^2x) = cos^2x

    We now have:

    cos^2x/sinx = the right side

    Done!

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