How do you verify the identity: $(cot(t)-tan(t))/(sin(t)cos(t)) = csc^2 (t) - sec^2 (t)$ ?

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Answer 1 · 2015-06-09T03:15:24

Verify the identity: $(cot t - tan t)/(sin t.cos t)$

$((cos t/sin t) - (sin t/cos t))/(sin t.cos t) =$

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

$= csc^2 t - sec^2 t$

How do you verify the identity: (cot(t)-tan(t))/(sin(t)cos(t)) = csc^2 (t) - sec^2 (t)(cot(t)-tan(t))/(sin(t)cos(t)) = csc^2 (t) - sec^2 (t)?