Answer
The trigonometric Identity is verified.
$sin^2α-sin^4α=cos^2α-cos^4α$
Work Step by Step
We know that:
$cos^2α+sin^2α=1$
$sin^2α=1-cos^2α$
Start al the left side of the equation:
$sin^2α-sin^4α=sin^2α-(sin^2α)^2=1-cos^2α-(1-cos^2α)^2=1-cos^2α-(1-2~cos^2α+cos^4α)=1-cos^2α-1+2~cos^2α-cos^4α=cos^2α-cos^4α$
