College Algebra & Trigonometry, 2018a

10.1. RECIPROCAL AND PYTHAGOREAN IDENTITIES 445
After we cancel out the sin 2 θ, we’re almost done:
✘✘✘
sin 2 θ
cos 2 θ · 1
✘✘✘
sin 2 θ − cot2 θ = sec 2 θ − cot 2 θ
1
cos 2 θ − cot2 θ = sec 2 θ − cot 2 θ
sec 2 θ − cot 2 θ = sec 2 θ − cot 2 θ
The trigonometric identities we have discussed in this section are summarized
below:
Pythagorean Identities
Reciprocal Identities
sin 2 θ +cos 2 θ =1
tanθ = sin θ
cos θ
tan 2 θ + 1 = sec 2 θ
cot θ = cos θ
sin θ
1+cot 2 θ = csc 2 θ sec θ = 1
cos θ
csc θ = 1
sin θ
In the examples above and in the exercises, the form sin θ or cos θ is typically used,
however any letter may be used to represent the angle in question so long as it is
the SAME letter in all expressions. For example, we can say that:
sin 2 θ +cos 2 θ =1
or we can say that