Trig Proving Identities help?

Prove the identity:

(cosθ - sinθ) / cosθ + sinθ) = sec 2θ - tan 2θ

please show work, thanks so much!

WILL AWARD BEST ANSWER!!!

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  • DWRead
    Lv 7
    6 months ago
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  • 6 months ago

    Multiply numerator and denominator by the conjugate of the denominator which is (cosθ - sinθ).

    This gives: [(cosθ)^2 - 2sinθcosθ + (sinθ)^2] / [(cosθ)^2 - (sinθ)^2] =

    [1 - 2sinθcosθ] / [cos2θ] = sec2θ - tan2θ

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