How to simplify

4sin[pi/2 + x] ?

using

sin(A+B) = sinAcosB + cosAsinB

4sin(π/2+x)
= 4(sin(π/2)cosx + cos(π/2)sinx)
= 4( (1)cosx + (0)sinx)
= 4 cosx

Thank you!

To simplify the expression 4sin[pi/2 + x], we can make use of the trigonometric identities. Specifically, the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b).

Let's apply this identity to the given expression:

4sin[pi/2 + x] = 4(sin(pi/2)cos(x) + cos(pi/2)sin(x))

Since sin(pi/2) equals 1 and cos(pi/2) equals 0, the expression simplifies to:

4(1cos(x) + 0sin(x)) = 4cos(x)

Therefore, the simplified form of 4sin[pi/2 + x] is 4cos(x).