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Prove: [(tan^2theta+1)(cos^2theta-1)]=1-sec^2theta

  • Math -

    tan^2 = sin^2/cos^2 = s^2/c^2

    (s^2/c^2+1)(c^2-1) = s^2 -s^2/c^2 +c^2 -1
    but s^2 + c^2 = 1
    so we have
    -s^2/c^2
    = -(1 - c^2)/c^2
    = - 1/c^2 + 1
    = 1 - sec^2

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