Question

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

Answer 1

you know that \[\sin^{4}\theta = (\sin^{2}\theta)^{2}\]
\[\cos^{4}\theta = (\cos^{2}\theta)^{2}\]

you know
\[\sin^{2}\theta=1-\cos^{2}\theta\]
\[\cos^{2}\theta = 1-\sin^{2}\theta\]
by using the identity
\[\sin^{2}\theta+\cos^{2}\theta=1\]

it is just a matter of substituting in what you know and simplifiying

Answer 2

thank you!