Show that `cos^(4)alpha+2cos^(2)alpha(1-(1)/(sec^(2)alpha))=1-sin^(4)alpha`

Show that cos ^(4) alpha + 2 cos ^(2) alpha (1-(1)/(sec ^(2) alpha ))=(1- sin ^(4) alpha )

To prove ((1)/(sec^(2)alpha-cos^(2)alpha)+(1)/(cos ec^(2)alpha-sin^(2)alpha))cos^(2)alpha sin^(2)alpha=(1-sin^(2)alpha cos^(2)alpha)/(2+sin^(2)alpha cos^(2)alpha)

( cos 2 alpha)/( cos^(4) alpha - sin^(4) alpha ) -(cos^(4) alpha + sin^(4) alpha )/(2-sin^(2) 2alpha ) =

If a is any real number then :(sin^(4)alpha+sin^(2)alpha*cos^(2)alpha+cos^(2)alpha)/(sin^(2)alpha+sin^(2)alpha*cos^(2)alpha+sin^(2)alpha)=

cos^(4)alpha+sin^(4)alpha-6sin^(2)alpha cos^(2)alpha=

2sec^(2)alpha-sec^(4)alpha-2cos ec^(2)alpha+cos ec^(4)alpha=cot^(4)alpha-tan^(4)alpha

sin alpha-cos alpha=(1)/(3) then sin^(4)alpha-cos^(4)alpha=

((1)/(sec^(2)alpha-cos^(2)alpha)+(1)/(cos ec^(2)alpha-sin^(2)alpha))cos^(2)alpha*sin^(2)alpha=(1-cos^(2)alpha*sin^(2)alpha)/(2+cos^(2)alpha*sin^(2)alpha)

Prove that sin^(4) alpha + cos^(4) alpha + 2 sin^(2) alpha cos^(2) alpha = 1 .

If (cos^(4)alpha)/(cos^(2)beta)+(sin^(4)alpha)/(sin^(2)beta)=1, then provet that (cos^(4)beta)/(cos^(2)alpha)+(sin^(4)beta)/(sin^(2)alpha)=1.