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Trig

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Verify that each of the following is an identity.

tan^2x-sin^2x=tan^2xsin^2x

I can get it down to cos^2 on the right, but cannot get it to work out on the left.

secx/cosx - tanx/cotx=1

On the left I got down to 1-tan^2, but that clearly doesn't equal 1....

1-2cos^2x/sinxcosx=tanx-cotx

I'm really not sure where to go with this one. Any help would be appreciated. Thanks in advance.

  • Trig - ,

    For the first, I am going to start on the left
    LS = sin^2 x/cos^2 x - sin^2 x
    = (sin^2 x - sin^2 xcos^2 x)/sin^2 x
    = sin^2x(1 - cos^2 x)/sin^2 x
    = (sin^2 x)(sin^2 x)/cos^2 x
    = tan^2 x sin^2 x
    = RS

    for the second

    LS = 1/cos^2 x - (sinx)/cosx)]/[cosx/sinx)]
    = 1/cos^2 x - sin^2 x/cos%2 x
    = (1 - sin^2 x)/cos^2 x
    = cos^2 x/cos^2 x
    = 1
    = RS

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