C H A P T E R 5 Analytic Trigonometry

446 Chapter 5 Analytic Trigonometry
80. Let x 2 sec . 81. Let x 5 tan , then
x 2 4 2 sec 2 4
4sec 2 1
4 tan 2
2 tan
x 2 25 5 tan 2 25
25 tan 2 25
25tan 2 1
25 sec 2
5 sec .
82. Let x 10 tan . 83. Let then 9 x becomes
2 x 3 sin ,
3
84.
86.
x 2 100 10 tan 2 100
x 6 sin
3 36 x 2
100tan 2 1
100 sec 2
10 sec
36 6 sin 2
361 sin 2
36 cos 2
6 cos
cos 3 1
6 2
sin ±1 cos 2
± 1 1
2 2
± 3
4
± 3
2
x 10 cos
53 100 x 2
100 10 cos 2
1001 cos 2
100 sin 2
10 sin
sin 53
10
3
2
cos 1 sin 2
1 3
2 2
1
2
87.
9 3 sin 2 3
9 9 sin 2 3
91 sin 2 3
9 cos 2 3
3 cos 3
cos 1
sin 1 cos 2
sin 1 cos 2 1 1 2 0.
85. Let then 16 4x becomes
2 x 2 cos ,
22
16 42 cos 2 22
Let y1 sin x and y2 1 cos2 x, 0 ≤ x ≤ 2.
y1 y2 for 0 ≤ x ≤ , so we have
sin 1 cos 2 for 0 ≤ ≤ .
0
16 16 cos 2 22
161 cos 2 22
2
−2
16 sin 2 22
4 sin 22
sin 2
2
cos 1 sin
1
1
2
2
y 2
y 1
1
2
2
2 .
2