Question

How do you prove `sin^4theta-cos^4theta=sin^2theta-cos^2theta`?

Answer 1

`sin^4 theta-cos^4 theta = sin^2 theta-cos^2 theta`

Left Side:`=sin^4 theta-cos^4 theta`

`=(sin^2theta-cos^2theta)(sin^2theta+cos^2theta)`

`=(sin^2theta-cos^2theta)*1`

`=sin^2theta-cos^2theta`

`=` Right Side