Question

Verify the identity.

sin 4u = 2 sin 2u cos 2u

and

cos ( x + pi/2) = -sin x

Answer 1

second one you can use the "addition angle" formula \[\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)\]

Answer 2

you get
\[\cos(x+\frac{\pi}{2})=\cos(x)\cos(\frac{\pi}{2})-\sin(x)\sin(\frac{\pi}{2})\]
\[=\cos(x)\times 0-\sin(x)\times 1=-\sin(x)\]

Answer 3

would cos ( x + pi/2) = -sinx = -sin x=sin(x)

Answer 4

so what is the first one

Answer 5

and is that your final answer for the second one

Answer 6

\[\sin(2x)=2\cos(x)\sin(x)\] replace \(x\) by \(2u\)

Answer 7

and this is for the first one or the second one