College Trigonometry, 2011a

10.4 Trigonometric Identities 789
54. ˆ sin(2θ) = 24
25
ˆ sin ( )
θ 2 √ 5
2 =
5
55. ˆ sin(2θ) =− 120
169
ˆ sin ( √
)
θ 26
2 =
26
56. ˆ sin(2θ) =− 120
169
ˆ sin ( )
θ 5 √ 26
2 =
26
ˆ cos(2θ) =− 7 25
ˆ cos ( √
)
θ 5
2 = −
5
ˆ cos(2θ) = 119
169
ˆ cos ( θ
2
)
= −
5 √ 26
26
ˆ cos(2θ) = 119
169
ˆ cos ( √
)
θ 26
2 =
26
ˆ tan(2θ) =− 24 7
ˆ tan ( θ
2)
= −2
ˆ tan(2θ) =− 120
119
ˆ tan ( )
θ 1
2 = −
5
ˆ tan(2θ) =− 120
119
ˆ tan ( θ
2)
=5
57. ˆ sin(2θ) =− 4 5
ˆ sin ( √ √
)
θ 50 − 10 5
2 =
10
ˆ cos(2θ) =− 3 5
ˆ cos ( √ √
)
θ 50 + 10 5
2 = −
10
ˆ tan(2θ) = 4 3
ˆ tan ( )
θ
√5 − √ 5
2 = −
5+ √ 5
tan ( )
θ 5 − 5 √ 5
2 =
10
58. ˆ sin(2θ) =− 4 5
ˆ sin ( √ √
)
θ 50 + 10 5
2 =
10
ˆ cos(2θ) =− 3 5
ˆ cos ( √ √
)
θ 50 − 10 5
2 =
10
ˆ tan(2θ) = 4 3
ˆ tan ( )
θ
√5+ √ 5
2 =
5 − √ 5
tan ( )
θ 5+5 √ 5
2 =
10
74.
77.
cos(2θ) + cos(8θ)
2
cos(4θ) + cos(8θ)
2
80. 2 cos(4θ) cos(θ)
75.
cos(5θ) − cos(9θ)
2
cos(θ) − cos(5θ)
78.
2
( ) ( )
9 5
81. −2cos
2 θ sin
2 θ
83. 2 cos(4θ)sin(5θ) 84. √ (
2cos θ − π )
4
76.
sin(8θ)+sin(10θ)
2
sin(2θ)+sin(4θ)
79.
2
( ) ( )
11 1
82. 2 sin
2 θ sin
2 θ
85. − √ 2sin
(
θ − π )
4
90. 1 − x2
2
91.
14x
x 2 +49
92. ln |x + √ x 2 +16|−ln(4)