C H A P T E R 5 Analytic Trigonometry

53.
54. Let
55.
57.
59.
cosarccos x arcsin x cosarccos x cosarcsin x sinarccos x sinarcsin x
0
(Use the triangles in Exercise 51.)
u
x 1 x 2 1 x 2 x
u arccos x and v arctan x
cos u x tan v x.
1
x
1 − x 2
cosarcos x arctan x cosu v
cos u cos v sin u sin v
x
1
1 x2 1 x2 x 1
x2 x x1 x2
1 x 2
sin3 x sin 3 cos x sin x cos 3
sin
6
0cos x 1sin x
sin x
x sin
6
cos sin
60. tan
4
1
cos x 3 sin x
2
2
v
1 + x 2
1
x
56.
cos x cos sin x 58.
6
cos cos sin sin sin
2
0
tan
tan
4
1 tan
tan
4
cos cos
Section 5.4 Sum and Difference Formulas 481
sin
2
cos 5
4
1cos 0sin 1cos sin 0
1 tan
1 tan
x sin cos x sin x cos
2 2
1cos x sin x0
cos x
x cos 5
4
cos cos sin
2
5
cos x sin sin x
4
2
cos x sin x
2