Question

Sin^8-cos^8=(sin^4+cos^4)(sin+cos)(sin-cos) prove
?

Answer 1

L.H.S

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

= (sin^4+cos^4)(sin^2+cos^2)

= sin^4(sin^2-cos^2)-cos^4(sin^2-cos^2)

= sin^4-cos^4.....

R.H.S

= (sin^8-cos^8)

= (sin^4+cos^4)(sin^4+cos^4)

= sin^4+cos^4......

Hence Proved!

L.H.S=R.H.S