## allison_ Group Title Verify the identity. cos 4x + cos 2x = 2 - 2 sin^2 2x - 2 sin^2 x one year ago one year ago

1. Tushara Group Title

cos(4x)=cos(2x+2x) expand that^

2. ajprincess Group Title

$$\cos4x=1-2\sin^2 2x$$ $$\cos2x=1-2\sin^2x$$ does that help?

3. allison_ Group Title

It did, but could you please show me how cos 4x = 1 - 2 sin^2 2x?

4. ajprincess Group Title

ya sure. $$\cos4x=\cos(2x+2x)$$ $$=\cos2x\cos2x-\sin2x\sin2x$$ $$=\cos^2 2x-\sin^2 2x$$ $$=1-\sin^2 2x-\sin^2 2x$$ $$(\cos^2 2x=1-\sin^2 2x)$$ $$=1-2\sin^2 2x$$

5. allison_ Group Title

Do you have a reference where it says cos^2 2x = 1−sin^2 2x? I think it would be useful for me since I have a formula sheet but I don't see that on here...

6. ajprincess Group Title

$$\cos^2x+\sin^2x=1$$ Similarly $$\cos^2 2x+\sin^2 2x=1$$ $$\cos^2 2x=1-\sin^2 2x$$

7. allison_ Group Title

Thank you for your time and assistance. :)

8. ajprincess Group Title

Welcome:)