sec theta-tan theta / sec theta + tan theta = 1- 2sec theta tan theta + 2 tan ^ 2

Please prove above equation by using trigo identity
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1 Answer

secθ-tanθ=1/cosθ-sinθ/cosθ=(1-sinθ)/cosθ;

secθ+tanθ=1/cosθ+sinθ/cosθ=(1+sinθ)/cosθ.

(secθ-tanθ)/(secθ+tanθ)=(1-sinθ)/(1+sinθ)=

(1-sinθ)2/(1-sin2θ)=(1-2sinθ+sin2θ)/cos2θ=

sec2θ-2secθtanθ+tan2θ=1+tan2θ-2secθtanθ+tan2θ=

1-2secθtanθ+2tan2θ QED.

by Top Rated User (1.2m points)

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