Question

hey...

prove that...

${sin}^{4} a + {cos}^{4} a = 1 - 2 {sin}^{2} a \: {cos}^{2} a$

Answer 1

sin^4 a+ cos^4 a = (sin^2a)^2 + (cos^2 a)^2
AS ( a^2 +b^2) = ( a+b)^2 - 2ab

SO, ( sin^2a+ cos^2a) - 2 sin^2acos^2a

AS sin^2a + cos^2 a = 1

So it's 1 - 2 sin^2a cos^2 a

Hope it will help u

Answer 2

$lhs = \\ { \sin }^{4} \alpha + { \cos }^{4} \alpha \\ ( { \sin }^{2} \alpha + { \cos \alpha }^{2} ) - 2 { \sin }^{2} \alpha \: { \cos }^{2} \alpha = rhs \: \\ proved$