Question #08381

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Answer 1 · 2017-03-21T22:59:42

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Remember $cot(x) = cos(x)/sin(x)$

$((cos^2(x)/sin^2(x))cos^2(x))/((cos^2(x)/sin^2(x))-cos^2(x))$

$((cos^2(x)/sin^2(x))(cos^2(x)/1))/((cos^2(x)/sin^2(x))-((cos^2(x)sin^2(x))/sin^2(x))$

$(cos^4(x)/sin^2(x))/((cos^2(x)-sin^2(x)cos^2(x))/sin^2(x))$

$cos^4(x)/(cos^2(x)-sin^2(x)cos^2(x))$

$cos^4(x)/(cos^2(x)(1-sin^2(x))$

$cos^2(x)/(1-sin^2(x))$

Use trig identities, specifically:
$sin^2(x)+cos^2(x)=1$
$cos^2(x)=1-sin^2(x)$

$cos^2(x)/cos^2(x)$

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Answer 2 · 2017-03-27T16:32:33

$(cot^2xcos^2x)/(cot^2x-cos^2x)$

$=((csc^2x-1)cos^2x)/(cot^2x-cos^2x)$

$=((1/sin^2x-1)cos^2x)/(cot^2x-cos^2x)$

$=(cos^2x/sin^2x-cos^2x)/(cot^2x-cos^2x)$

$=(cot^2x-cos^2x)/(cot^2x-cos^2x)=1$