Provev that:cos2x/cosx-sinx=cosx+sinx?

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Provev that:cos2x/cosx-sinx=cosx+sinx?

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Answer 1 · 2018-05-20T08:48:59

$see explanation$ $"see explanation"$

Explanation:

$using the trigonometric identity$ $"using the "color(blue)"trigonometric identity"$

$∙ x cos 2 x = {cos}^{2} x - {sin}^{2} x$ $•color(white)(x)cos2x=cos^2x-sin^2x$

$consider the left side$ $"consider the left side"$

$\frac{{cos}^{2} x - {sin}^{2} x}{cos x - sin x}$ $(cos^2x-sin^2x)/(cosx-sinx)$

${cos}^{2} x - {sin}^{2} x is a difference of squares$ $cos^2x-sin^2x" is a "color(blue)"difference of squares"$

$=(cancel((cosx-sinx))(cosx+sinx))/cancel(cosx-sinx)$

$=cosx+sinx=" right side "rArr"verified"$

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Provev that:cos2x/cosx-sinx=cosx+sinx?

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