Question

does cos^2 - sin^2 = 2cos^2 - 1?

Answer 1

By the Pythagorean Theorum, \(\sin^2 + \cos^2 = 1\). Is there a way you can use that to simplify your equation?

Answer 2

i was thinking about that but i wasn't sure and this is just the last step of my equation but yea

Answer 3

One way to make it clear might be to say:
Let \(X = \cos^2\)
Let \(Y = \sin^2\)
Now, your question would be:
Does \(X - Y = 2X - 1\)? (given that we know \(X+Y = 1\))

Answer 4

that sounds helpful

Answer 5

\[\cos \left( A+B \right)=\cos A \cos B-\sin A \sin B\]
If B=A
\[\cos \left( A+A \right)=\cos A \cos A-\sin A \sin A=\cos ^2A-\sin ^2A\]
\[\cos ^2A+\sin ^2A=1,\sin ^2A=1-\cos ^2A\]
?

Answer 6

thank you for that but i dont think that helps my situation right now ;/

Answer 7

\[\cos ^2A-\sin ^2A=\cos ^2A-(1-\cos ^2A)=\cos ^2A-1+\cos ^2A=2 \cos ^2 A-1\]