How do you prove $(Cot(x) - tan(x)) /( sin(x) cos(x)) = csc^2(x) - sec^2(x)$ ?

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Answer 1 · 2016-05-05T20:46:15

see below

Left Side: $=(cosx/sinx -sinx/cosx)/(sinxcosx)$

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

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

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

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

$=1/sin^2x - 1/cos^2x$

$=csc^2x-sec^2x$

$=$ Right Side

How do you prove (Cot(x) - tan(x)) /( sin(x) cos(x)) = csc^2(x) - sec^2(x)(Cot(x) - tan(x)) /( sin(x) cos(x)) = csc^2(x) - sec^2(x)?