How do you verify the identity $1-tan^4theta=2sec^2theta-sec^4theta$ ?

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Answer 1 · 2016-09-07T14:38:40

See the Explanation.

We will use the Identity $: sec^2x=1+tan^2x$ .

$"The R.H.S."=2sec^2theta-sec^4theta$

$=sec^2theta(2-sec^2theta)$

$=(1+tan^2theta){1+(1-sec^2theta)}$

$=(1+tan^2theta){1-(sec^2theta-1)}$

$=(1+tan^2theta)(1-tan^2theta)$

$=1^2-(tan^2theta)^2$

$=1-tan^4theta$

$"=The L.H.S."$

How do you verify the identity 1-tan^4theta=2sec^2theta-sec^4theta1-tan^4theta=2sec^2theta-sec^4theta?