How do you simplify the expression $(cot^2tcos^2t)/(cot^2t-cos^2t)$ ?

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Answer 1 · 2016-09-29T05:49:19

1

Since $cot t=cos t/sin t$ , let's substitute to have:

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

that's

$(cos^4t/cancel(sin^2t))/((cos^2t-sin^2tcos^2t)/cancel(sin^2t))$

$=cos^4t/(cos^2t(1-sin^2t)$

that's, since $1-sin^2t=cos^2t$ ,

$cos^4t/cos^4t=1$

How do you simplify the expression (cot^2tcos^2t)/(cot^2t-cos^2t)(cot^2tcos^2t)/(cot^2t-cos^2t)?