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1-tan^2 theta/1+tan^2 theta + 2sin^2 theta need to simply to sin and cos

  • math -

    I have a strong feeling you meant:

    (1-tan^2 Ø)/(1 + tan^2Ø) + 2tan^2 Ø
    = (1 - sin^2 Ø/cos^2 Ø)/sec^2 Ø + 2sin^2 Ø/cos^2 Ø
    = (1 - sin^2 Ø/cos^2 Ø)(cos^2 Ø) + 2sin^2 Ø/cos^2 Ø
    = cos^2 Ø - sin^2 Ø + 2sin^2 Ø/cos^2 Ø
    this is in terms of sines and cosines

    we could write it as

    cos (2Ø) - 2sin^2 Ø/cos^2 Ø

    anything beyond that would only make it more complicated.

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