Formulas for sin and cos

Yayy for no school tomorrow!
But we still have to blog.. :/
Haha, anywayysss.....

Formulas:
--Sum and Difference Formulas for Cosine and Sine
*cos(theta+/-B)=cos(theta)cos(B)-/+sin(theta)sin(B)
*sin(theta+/-B)=sin(theta)cos(B)+/-cos(theta)sin(B)

--Rewriting a Sum or Difference as a Product
sinx+siny=2sin((x+y)/2)cos((x-y)/2)
sinx-siny=2cos((x+y)/2)sin((x+y)/2)
cosx+cosy=2cos((x+y)/2)cos((x+y)/2)
cosx-cosy=-2sin((x+y)/2)sin((x-y)/2)

--The two main purposes for the addition formulas are:
1) To find the exact values of trigonometric expressions
2) Simplifying expressions to obtain other identities.

--The sum or difference formulas can be used to verify many identities that we have seen, and also to derive new identites.

^^that looks veryyyyy complicated, but it's not.

Example 1:
Simplify the given expression.
sin75degrees(cos15degrees)+cos75degrees(sin15degrees)
sin(75degrees+15degrees)=sin90degrees=1

Example 2:
Simplify the given expression.
cos5pi/12(cospi/12)-sin5pi/12(sinpi/12)
cos(5pi/12+pi/12)=cos6pi/12=cospi/2=0

Example 3:
Simplify the given expression.
sin3x(cos2x)-cos3x(sin2x)
sin(3x-2x)=sinx

Example 4:
Find the exact value of each expression.
cos105degrees
cos(60degrees+45degrees)=cos60degrees(cos45degrees)-sin60degrees(sin45degrees)
(1/2)(square root of 2/2)-(square root of 3/2)(square root of 2/2)
square root of 2/2-square root of 6/2=square root of 2-square root of 6/4

Example 5:
Simplify the given expression.
cos105degrees(cos15degrees)+sin105degrees(sin15degrees)
cos(105degrees-15degrees)=cos95degrees

Example 6:
Simplify the given expression.
sin4pi/3(cospi/3)-cos4pi/3(sinpi/3)
sin(4pi/3-pi/3)=sin5pi/3

Example 7:
Simplify the given expression.
cos2x(cosx)+sin(2x)sinx
cos(2x-x)=cosx