Help - trig identities (1 Viewer)

[simDS]

can somwone please help

prove sin^4 theta - cos^4 theta = 2sin ^2 theta - 1

thanks

 

[hollownomore]

prove sin^4 theta - cos^4 theta = 2sin ^2 theta - 1

Answer:

sin^4 theta - cos^4 theta = (sin^2 theta + cos^2 theta)x
(sin^2 theta - cos^2 theta)
(difference of two squares)
= (1)(sin^2 theta - cos^2 theta)
= sin^2 theta - cos^2 theta
= sin^2 theta - (1 - sin^2 theta)
= 2sin^2 theta - 1 as required

Good Luck!

hollownomore.