Trig

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Claim: For all theta such that
-pie/2<theta<pie/2 the following holds true:
(1+tan(theta))^2=1/cos(theta)

  • Trig -

    LS = (1+ tanØ)^2
    = 1 + 2tanØ + tan^2 Ø
    = 1 + 2tanØ + sec^2 Ø - 1
    = 2sinØ/cosØ + 1/cos^2 Ø
    = (2sinØcosØ + 1)/cos^2 Ø
    = (sin^2 Ø + cos^2 Ø + 2sinØcosØ)/cos^2 Ø
    = (sinØ + cosØ)^2 /cosØ
    ≠ RS

    The identity is false , all we need is one example when it does not work

    e.g. Ø=30°
    LS = (1+tan30°)^2 = appr 2.488
    RS = 1/cos30° = 1.15

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