College Algebra & Trigonometry, 2018a

456 CHAPTER 10. TRIGONOMETRIC IDENTITIES AND EQUATIONS
Here is a summary of all the identities we’ve worked with in this chapter:
Pythagorean Identities
sin 2 θ +cos 2 θ =1
tan 2 θ + 1 = sec 2 θ
Reciprocal Identities
tanθ = sin θ
cos θ
cot θ = cos θ
sin θ
1+cot 2 θ = csc 2 θ sec θ = 1
cos θ
Double-Angle Identities
cos(2θ) =cos 2 θ − sin 2 θ
cos(2θ) =2cos 2 θ − 1
cos(2θ) =1− 2sin 2 θ
sin(2θ) =2sinθ cos θ
csc θ = 1
sin θ
Working problems involving double-angle identities is very similar to the other
identities we’ve worked with previously - you just have more identities to choose
from!
Example
Verify the given identity: cos 2x = 1−tan2 x
1+tan 2 x
We have three possible identities to choose from for the left-hand side, so we’ll
wait on that for a moment while we simplify the right-hand side.