\(sin^4a+cos^4a=\left(sin^2a+cos^2a\right)^2-2sin^2a.cos^2a=1-2sin^2a.cos^2a\)
\(sin^4a-cos^4a=\left(sin^2a-cos^2a\right)\left(sin^2a+cos^2a\right)=sin^2a-cos^2a\)
\(=1-cos^2a-cos^2a=1-2cos^2a\)
\(tan^2a-sin^2a=\dfrac{sin^2a}{cos^2a}-sin^2a=sin^2a\left(\dfrac{1}{cos^2a}-1\right)=\dfrac{sin^2a\left(1-cos^2a\right)}{cos^2a}=\dfrac{sin^2a}{cos^2a}.sin^2a=tan^2a.sin^2a\)