How do you verify the identity $-2cos^2theta=sin^4theta-cos^4theta-1$ ?

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Answer 1 · 2016-10-07T16:10:09

see below bolded text

$-2cos ^2 theta=sin^4 theta-cos^4theta-1$

Right Side : $=sin^4 theta-cos^4theta-1$

$=(sin^2theta-cos^2theta)(sin^2theta+cos^2theta)-1$

$=(sin^2theta-cos^2theta) *1 - 1$

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

$=1-cos^2theta-cos^2theta-1$

$=cancel1-2cos^2theta-cancel 1$

$=-2cos^2theta$

$:.=$ Left Side

How do you verify the identity -2cos^2theta=sin^4theta-cos^4theta-1-2cos^2theta=sin^4theta-cos^4theta-1?