IDENTITIES

Steps to finding identities:

• Algebra
• Pythagorean formulas, if not, convert to sin and cos
• Algebra
• Continue steps 1-3

Pythagorean identities are:

1. Sin ^2 theta + Cos ^2 theta = 1
2. 1 + Tan ^2 theta = Sec ^2 theta
3. 1 + Cot^2 theta = Csc ^2 theta

Reciprocal identities are:

• CscX = 1/SinX
• SecX = 1/CosX
• CotX= 1/TanX

Example... Simplify

Sec x - Sin x Tan x

= 1/ Cos x - Sin x ( Sin x/ Cos x)

= 1/ Cos X - Sin ^2 x/ Cos x = 1- Sin ^2 x/ Cos x

= Cos ^2 x/ Cox x = Cos x

1) Changed Sec to 1/cos. Changed Tan to Sin/Cos

2) Multiplied Sin x by whatever was in the parenthesis

3) Used the pythagorean identity Sin^2 theta+Cos^2 theta=1

4) Reduced