HAAT - Mr. Hayes
7.2 - Verifying Trig Identities
Retake Review
Name: ___________________________________
Date: ______________________
As always, please show work when appropriate. See Mr. Hayes and your book if you need help.
3.0 Questions
5.0 Questions
8)
Factor the trigonometric expression.
sin2 x - 1
1)
sin x + 1
2)
9) sec 4 x - tan 4 x = sec 2 x + tan 2 x
csc x (sin 2 x + cos2 x tan x)
sin x + cos x
10)
Use the fundamental identities to simplify the expression.
cos2 θ
+ csc θ sin θ
3)
sin2 θ
4)
sin x cos x
tan x
Verify that each equation is an identity.
5) csc2 t - cos t sec t= cot2 t
6) sec β + tan β = 7)
tan x + cot x
1
= tan x - cot x
2
sin x - cos2 x
cos β
1 - sin β
sec θ - 1
tan θ
= tan θ
sec θ + 1
1
sin x + cos x 1 + 2 sin x cos x
= sin x - cos x
2 sin 2 x - 1
Answer Key
Testname: 7.2
1) sin x - 1
2) 1
3) csc2 θ
4) cos2 x
1
= csc2 t - 1 =
5) csc2 t - cos t sec t = csc2 t - cos t · cos t
cot2 t
6) sec β + tan β = sin β 1 + sin β 1 + sin β
1
+ = = ·
cos β
cos β
cos β cos β
1 - sin2 β
cos2 β
1 - sin β
= = =
1 - sin β cos β(1 - sin β) cos β(1 - sin β)
cos β
1 - sin β
7)
sec θ - 1 sec θ - 1 sec θ + 1
sec2 θ - 1
= · = =
tan θ
tan θ
sec θ + 1 tan θ(sec θ + 1)
tan θ
tan2 θ
= tan θ(sec θ + 1) sec θ + 1
8)
sin x cos x
+ cos x sin x
sin2 x + cos2 x
cos x sin x
tan x + cot x
= = =
sin x cos x
tan x - cot x
sin2 x - cos2 x
- cos x sin x
cos x sin x
1
sin2 x + cos2 xx
= 2
2
2
sin x - cos2 x
sin x - cos x
9) sec 4 x - tan 4 x = (sec 2 x + tan 2 x)(sec 2 x - tan 2 x)
= (sec 2 x + tan 2 x)(1) = sec 2 x + tan 2 x.
10)
sin x + cos x
sin x + cos x sin x + cos x
= =
sin x - cos x
sin x + cos x sin x - cos x
sin 2 x + 2 cos x sin x + cos 2 x
=
sin 2 x - cos 2 x
1 + 2 sin x cos x
1 + 2 cos x sin x
= .
2
2
2 sin 2 x - 1
sin x + sin x - 1
2