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Verify: (tanx-cotx)/(tanx+cotx) + 2cos^(2)x = 1?

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Verify: (tanx-cotx)/(tanx+cotx) + 2cos^(2)x = 1?

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  1. (tanx-cotx)/(tanx+cotx) + 2cos^(2)x =

    (tanx - 1/tanx) / (tanx + 1/tanx) + 2cos^(2)x =

    (tan^2x-1 / tan^2x+1) + 2cos^(2)x =

    tanx = sinx/cosx

    (sin^2x/cos^2x - 1) / (sin^2x/cos^2x +1) + 2cos^(2)x =

    (sin^2x-cos^2x/cos^2x) / (sin^2x+cos^2x/cos^2x) +2cos^(2)x =

    (sin^2x-cos^2x) /  (sin^2x+cos^2x) + 2cos^(2)x  =

    (sin^2x-cos^2x) / 1 + 2cos^(2)x =

    sin^2x + cos^2x = 1

    Maybe there's another shorter way to do this, but I hope this helps.

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