10-1

Last week I taught you all some formulas for trig equations. Those were double and half angle formulas. This week I am going to teach you how solve trig equations by using addition and subtraction formulas. This is actually two different sections. One is for sine and cosine, while the other is for tangent.
These are the formulas:
1. cos (alpha +/- beta) = cos (alpha) cos (beta) -/+ sin (alpha) sin (beta)
2. sin (alpha +/- beta) = sin (alpha) cos (beta) +/- cos (alpha) sin (beta)
3. sin x + sin y = 2 sin ((x + y)/(2) cos ((x-y)/(2)
4. sin x - sin y = 2 cos ((x+y)/(2) sin ((x-y)/(2)
5. cos x + cos y = 2 cos ((x+y)/(2) cos ((x-y)/(2)
6. cos x - cos y = -2 sin ((x+y)/(2) sin ((x-y)/(2)
7. tan (alpha + beta)= ((tan alpha + tan beta)/(1- tan alpha tan beta))
8. tan (alpha – beta)= ((tan alpha – tan beta)/(1+ tan alpha tan beta))

Example:
Simplify: sin 75 degrees cos 15 degrees + cos 75 degrees sin 15 degrees
• =sin (75 degrees + 15 degrees)
• =sin (90 degrees)
• =1

-Braxton