How do you verify $sec^4x-sec^2x=tan^4x+tan^2x$ ?

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Answer 1 · 2015-11-07T05:16:13

Verify $sec^4 x - sec^2 x = tan ^4 x + tan^2 x$

Left side $->sec^4 x - sec^2 x$

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

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

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

$= tan^2 x(1/(cos^2 x))$

Apply the trig identity: $1/(cos^2 x) = (1 + tan^2 x)$ , we get:

Left side $-> tan^2 x(1 + tan^2 x)= tan^4 x + tan^2 x.$

How do you verify sec^4x-sec^2x=tan^4x+tan^2xsec^4x-sec^2x=tan^4x+tan^2x?