Question

prove that
sin^8A-cos^8A=(1-2cos^2A)(1-2sin^2A×cos^2A​

Answer 1

Answer:

Here is your answer ✌!

LHS,

sin^8a - cos^8a

( sin^4a )² - ( cos^4a )²

(sin^4a - cos^4a) (sin^4a + cos^4a)

[ (sin²a)² - (cos²a)² ] [ ( sin²a + cos²a) -

2sin²a cos²a ]

(sin²a + cos²a)(sin²a - cos²a) [ 1 - 2sin²a

cos²a ]

(sin²a - cos²a) ( 1 - 2sin²a cos²a )

we know , cos 2a = cos²a - sin²a

- cos 2a ( 1 - 2sin²a cos ²a )

And also, cos 2a = 2cos²a - 1

- ( 2cos²a - 1 ) ( 1 - 2sin²a cos²a )

( 1 - 2cos²a ) ( 1 - 2sin²a cos²a )

Hence proved

Hope it's help you ✌!