How do you verify $(cotx/sec^2x) + (cotx/csc^2x)= cotx$ ?

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Answer 1 · 2015-11-03T15:54:49

Verify trig expression.
$(cot x/sec^2 x) + (cot x/csc^2 x) = cot x$

First term of left side:
$((cos x/(sin x))/(1/(cos^2 x))) = (cos^3 x)/(sin x)$ (1)

Second term of left side:
$((cos x)/sin x)/(1/sin^2 x) = (cos x.sin^2 x) /(sin x)$ (2).

Add (1) and (2)
$((cos^3 x)/(sin x))+ (cos x sin^2 x)/(sin x) =$
$= (cos x)/(sin x)(cos^2 x + sin^2 x) = (cos x)/(sin x) = cot x$

Answer 2 · 2015-11-03T16:05:03

Determination is done by following method.

LHS= $cotx/sec^2x+cotx/csc^2x$

$" "color(white)(a)=cotx(1/sec^2x+1/csc^2x)$

$" "color(white)(a)=cotx(cos^2x+sin^2x)$

$" "color(white)(a)=cotx$

$" "color(white)(a)=RHS$

How do you verify (cotx/sec^2x) + (cotx/csc^2x)= cotx(cotx/sec^2x) + (cotx/csc^2x)= cotx?