## anonymous one year ago does cos^2 - sin^2 = 2cos^2 - 1?

1. Valpey

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

2. anonymous

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

3. Valpey

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 $$X+Y = 1$$)

4. anonymous

5. anonymous

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

6. anonymous

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

7. anonymous

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

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