Question

Verify the identity
cos 4u= cos^2u - sin^2u

Answer 1

You'll have to use the identities \(\large sin^2x= \frac{1}{2}(1-cos2x) \) and \(\large cos^2 x = \frac{1}{2}(1+cos2x)\)

Answer 2

Sorry it's
Cos 4u= cos^2(2u) -sin^2 (2u)

Answer 3

This is the double angle formula

Answer 4

multiplied by a factor of 2

Answer 5

Please keep in mind this identity:
\[\cos \left( {2x} \right) = {\left( {\cos x} \right)^2} - {\left( {\sin x} \right)^2}\]

Answer 6

OK so do I multiply everything by 2?

Answer 7

Would cos2 (2×) = 2 (cos x)^2 - 2 (sin x)^2 be right?

Answer 8

Please set x= 2u into my above identity

Answer 9

cos2 (2u) = (cos 2u)^2 - (sin 2u)^2

Answer 10

@Michele_Laino

Answer 11

yes! it is your dentity, since 2*2u=4u

Answer 12

oops..identity...

Answer 13

Oh so that's the answer? There's nothing else I need to do?

Answer 14

yes! that is the answer since you have showed that your originalk identity is true, and in order to that you ahve applied the subsequent identity:
\[\cos \left( {2x} \right) = {\left( {\cos x} \right)^2} - {\left( {\sin x} \right)^2}\]

Answer 15

oops...you have...

Answer 16

OK thank you!

Answer 17

thank you!