Question

cos^4t - sin^4t = 1-2sin^2t

Answer 1

Note that \(\cos^4t-\sin^4t=(\cos^2t-\sin^2t)(\cos^2t+\sin^2t)=\cos^2t-\sin^2t\) :)

Answer 2

@hartnn I thought you were answering lol

Answer 3

i was
but i knew you would answer it correctly
so i thought i was not needed anymore :)

Answer 4

oh thanks :)

Answer 5

And then add \(\sin^2t\) and subtract it again, so that makes:
\[\cos^2t+(\sin^2t-\sin^2t)-\sin^2t\]

Answer 6

Add the \(\cos^2t+\sin^2t\) together to make \(1\) :)

Answer 7

Complete proof:
\[\cos^4t-\sin^4t\]\[=(\cos^2t-\sin^2t)(\cos^2t+\sin^2t)\]\[=\cos^2t-\sin^2t\]\[=\cos^2t+\sin^2t-\sin^2t-\sin^2t\]\[=1-\sin^2t-\sin^2t\]\[=1-2\sin^2t\]
Hope I helped you :)

Answer 8

Thank you!