Verify the identities algebraically.

Question

1.) TAN^5 X= TAN³X SEC²X-TAN³X

2.) COS³X SIN²X= (SIN²X-SIN^4X)COS X

Answer 1

LS = cosx (cos^2 x) (sin^2 x)
= cosx (1 - sin^2 x) (sin^2 x)
= cosx(sin^2 x - sin^4 x)
= RS