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Can anyone help prove this trigonometric identity?

1 Answer

Shwetank Mauria

Mar 14, 2017

Please see below.

Explanation:

$\frac{{cos}^{2} θ - {sin}^{2} θ}{{cos}^{2} θ + sin θ cos θ}$ $(cos^2theta-sin^2theta)/(cos^2theta+sinthetacostheta)$

= $\frac{(cos θ + sin θ) (cos θ - sin θ)}{cos θ (cos θ + sin θ)}$ $((costheta+sintheta)(costheta-sintheta))/(costheta(costheta+sintheta))$

= $(cancel((costheta+sintheta))(costheta-sintheta))/(costhetacancel((costheta+sintheta)))$

= $(costheta-sintheta)/costheta$

= $costheta/costheta-sintheta/costheta$

= $1-tantheta$

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