Holiday..

Alright, so I think this is my third post of the holidays (not prompts).
Going back to Chapter 10 now..
Chapter 10 dealt with finding the exact value of cos, sin, and tan. In 10-1, we were given two formulas:
cos(alpha +/- beta) = cos alpha cos beta -/+ sin alpha sin beta
sin(alpha +/- beta) = cos alpha cos beta +/- cos apha cos sin beta

EXAMPLE 1: Show that sin (3pi/2 – x) = -cos
A). We see the left side of our sin formula here.. so lets expand it – sin 3pi/2 cos x - cox 3pi/2 sin x
B). Replace the 3pi/2 with numbers from your trig chart. *3pi/2 = 270 degrees
C). (-1) cos x - (0) sin x
D). - cos x = - cos x

EXAMPLE 2: Solve cos (90 degrees + theta) + cos (90 degrees - theta)
A). Expand the left and right side of the (+) – cos 90 degrees cos theta - sin 90 degrees sin theta + cos 90 degrees cos theta + sin 90 degrees sin theta
B). The -/+ sin 90 degrees sin theta cancels out and you’re left with cos 90 degrees cos theta + cos 90 degrees cos theta
C). 2(cos 90 degrees)(cos theta)
D). Plug in cos 90 degrees from your trig chart or unit circle.
E). 2(0)cos theta
F). Your answer is cos theta