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.#