How do I verify this equation is an identity? cos(x+y)/cosx cosy=1-tanx tany

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How do I verify this equation is an identity? cos(x+y)/cosx cosy=1-tanx tany

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Answer 1 · 2018-03-18T23:15:03

$see explanation$ $"see explanation"$

Explanation:

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

$∙ x cos (x + y) = cos x cos y - sin x sin y$ $•color(white)(x)cos(x+y)=cosxcosy-sinxsiny$

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

$\frac{cos (x + y)}{cos x cos y}$ $(cos(x+y))/(cosxcosy)$

$= \frac{cos x cos y - sin x sin y}{cos x cos y}$ $=(cosxcosy-sinxsiny)/(cosxcosy)$

$=cancel(cosxcosy)/cancel(cosxcosy)-(sinxsiny)/(cosxcosy)$

$=1-(sinx/cosx xxsiny/cosy)$

$=1-tanxtany=" right side "rArr"verified"$

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How do I verify this equation is an identity? cos(x+y)/cosx cosy=1-tanx tany

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