Question

SHOW THAT (sin power8 A -cos power8 A) = (2 sin power2 A - 1)(1 - 2 sin power2 A cos power 2 A). please do answer.......​

Answer 1

Answer:

Step-by-step explanation:

sin^8A-cos^8A

=(sin^4A+cos^4A)*(sin^4A-cos^4A)

=(sin^4A+cos^4A)*(sin^2A-cos^2A)*(sin^2A+cos^2A)

=(sin^4A+cos^4A)*(sin^2A-cos^2A)

=[ (sin^2A-cos^2A)^2-2sin^2Acos^2A ]*(sin^2A-(1-sin^2A)]

=(1- 2sin^2Acos^2A ) (2sin^2A-1)

=( 2sin^2A - 1) * ( 1- 2sin^2 Acos^2A )

hence proved