C H A P T E R 5 Analytic Trigonometry

43. (a)
(b)
(c)
45. (a)
47.
(b)
(c)
−2 2
Let and y2
Identity
1
tan x4. y1
1
sin x4 2
1
sin x2 Identity
−1
5 44. (a)
csc 4 x 2 csc 2 x 1 csc 2 x 1 2
y y 2 1
−2 2
cos x
Let y1
and y2
1 sin x
Not an identity
Not an identity
3
−3
cos x1 sin x
1 sin 2 x
cos x1 sin x
cos 2 x
cot 2 x 2 cot 4 x
cos x cos x 1 sin x
1 sin x 1 sin x 1 sin x
1 sin x
.
cos x
1 sin x
cos x
tan 3 x sec 2 x tan 3 x tan 3 xsec 2 x 1 48.
tan 3 x tan 2 x
tan 5 x
Section 5.2 Verifying Trigonometric Identities 455
(b)
(c)
46. (a)
(b)
−2 2
Identity
Identity
1
−1
sin 4 2 sin 2 1 cos sin 2 1 2 cos
−2 2
3
−5
Not an identity
cos 2 2 cos
cos 5
Not an identity
csc 1
(c) is the reciprocal of
cot
They will only be equivalent at isolated points in their
respective domains. Hence, not an identity.
.
cot
csc 1
tan 2 x tan 4 x sec 2 x sin2 x
cos 2 x sin4 x
cos 4 x 1
cos 2 x
1
cos 4 x sin2 x sin4 x
cos 2 x
1
cos4 x sin2 x cos2 x sin4 x
cos2 x
1
cos4 x sin2 xcos2 x sin2 x
cos2 x
1
cos 4 x sin2 x
cos 2 x 1 sec4 x tan 2 x