How do you verify the identity $sec^2thetasin^2theta=sec^4theta-(tan^4theta+sec^2theta)$ ?

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Answer 1 · 2016-10-07T19:26:15

see below

$sec^2 theta sin^2 theta= sec^4 theta-(tan^4 theta + sec^2 theta)$

Right Side : $=sec^4 theta-(tan^2 thetatan^2theta+sec^2theta)$

$=sec^4 theta-((sec^2-1)(sec^2theta-1) + sec^2theta)$

$=sec^4 theta-(sec^4theta-2sec^2theta+1+sec^2theta)$

$=sec^4 theta-(sec^4theta-sec^2theta+1)$

$=sec^4 theta-sec^4theta+sec^2theta-1$

$=sec^2 theta-1$

$=tan^2 theta$

$=sin^2 theta/cos^2 theta$

$=1/cos^2 theta sin^2theta$

$=sec^2 theta sin^2 theta$

$:.=$ Left Side

How do you verify the identity sec^2thetasin^2theta=sec^4theta-(tan^4theta+sec^2theta)sec^2thetasin^2theta=sec^4theta-(tan^4theta+sec^2theta)?