1. We did the derivation and proof in class on Monday that sin (a+b) = sin (a) cos (b) + cos(a) + sin (b)

here is a video of me doing the proof of the similar formula for cosine: cos (a+b) = cos(a) cos(b) - sin (a) sin (b)

2. Use the sum of angles formula for sine (see #1), and plug in theta for both a and b. Simplify

3.a. Start with the left side. Simplify. Use the Pythagorean identity (sin^2(x)+cos^2(x)=1). Get the right hand side.

b. Start with the left hand side. Distribute/FOIL. Simplify. Use the Pythagorean identity. Get right hand side.

c. Start with the Pythagorean identity. Divide everything by either sin^2 (x) or cos^2 (x) depending on which other version you are trying to get. Simplify slightly.

d. Plug x and 90 into the sin (a+b) formula. Plug in values for sin(90) and cos(90)