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

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

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

(1)/(sec^(4) alpha ) +(1)/("cosec"^(4) alpha ) +(2)/(sec^(2) alpha + "cosec"^(2) alpha )=

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

If sin^(16) alpha = (1)/(5) , then the value of (1)/( cos^(2) alpha) + (1)/( 1 + sin^(2) alpha) + (2)/( 1 + sin^(4) alpha) + (4)/( 1 + sin^(8) alpha) is

Prove that, 1/3 ( cos^(3) alpha sin 3 alpha + sin^(3) alpha cos 3 alpha) = 1/4 sin 4 alpha

IF sin ^(16) alpha = 1/5 then the value of (1) /(cos ^2 alpha) +(1)/( 1 + sin ^2 alpha) +(2)/(1+ sin ^4 alpha) + ( 4 )/( 1+ sin ^8 alpha) is equal to

cos alpha cos 2 alpha cos 4 alpha cos 8 alpha = (1)/(16), if alpha = 24 ^(@)

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)