Question

Verify the identity.

sin 4u = 2 sin 2u cos 2u

Answer 1

i have two other identities i need help with if you are good with them. im pretty much awful at identities so i really need help

Answer 2

This follows directly from the double angle formula:
\[\sin 2 \theta = 2 \sin \theta \cos \theta\] Plug in theta=2u and you have your answer.

Answer 3

but 2 * 2sin x cos x equals 4 sin x 2 cosx not 2 sin 2u cos 2 u
right? or are they the same thing

Answer 4

You're plugging in 2u for theta in the identity shown. This will give you 2sin(2u)cos(2u)

Answer 5

i still dont understand

Answer 6

Take this identity:
\[\sin 2 \theta = 2 \sin \theta \cos \theta\] and plug in 2u for theta:
\[\sin 2(2u) = 2 \sin (2u) \cos (2u)\]
\[\sin 4u = 2 \sin 2u \cos 2u\]

Answer 7

ok thankyou

Answer 8

sin 4u = 2 sin 2u cos 2u
sin 2u sin 2u = 2 sin 2u cos 2u
2sin u cos u 2 sin u cos u = 2 sin 2u cos 2u
2 sin 2u cos 2u = 2 sin 2u cos 2u
does this prove it correctly?

Answer 9

If you've learnt sin(A+B) = sinAcosB + cosAsinB,
sin(4u)
= sin(2u+2u)
= sin(2u)cos(2u) + cos(2u)sin(2u)
= 2 sin(2u) cos(2u).

Answer 10

see that makes much more since, thankyou