Question

Calculus Question:

I'm in the middle of solving a problem, although I was wondering how:

(hold on, I'm typing it in the equation formatter)

Answer 1

\[-\sin^2(t)+\cos^2(t)\] simplifies to:
\[\cos(2t)\]

Answer 2

Similarly,

\[-4\sin^2(t)+4\cos^2(t)\]
Simplifies to:
\[4\cos(2t)\]

How did that happen?

Answer 3

(Done typing question)

Answer 4

this is a known trig identity

cos2t = cos^t - sin^2t

Answer 5

Oh of course.... I didn't think of that. Thanks a lot!