13. (cot-tan 0)2(2+√3)=4(2−√3).

22. Solve m sin = 1.29743, and m cos = 6.0024.

23. Solve m sin = −0.3076258, and m cos p=0.4278735. Ans. 324° 17′ 6′′.6, m = 0.52698.

(m positive.)

24. Solve m sin p = 0.08219, and m cos = 0.1288.

25. Solve m sin = 194.683, and m cos &

c, and a cos 0 + b sin 0 = c sin 0

26. If a sin 0 + b cos 0 = cos 0, show that sin 20(c2 - a2 - b2) = 2 ab.

Solve the following equations:

П

27. √2 sin 0+√2 cos 0=√3. Ans. —+nπ + ( − 1)" ·

4

28. 2 sin x + 5 cos x = 2. Sug. [2.5 = tan 68° 12′].

Ans. x=- · 68° 12′ + n 180° + ( − 1)" (21° 48').

=

=

29. 3 cos x8 sina 3. Sug. [2.6 tan 69° 26' 30"]. Ans. x=- — 69° 26' 30" + 2 n 180° ± (69° 26' 30").

- 15 cos x =

30. 4 sin x

Ans.

= 4. Sug. [3.75 = tan 75° 4′].

x = 75° 4' + n 180° + ( − 1)" (14° 56′).

31. cos (a + x)=sin(a + x)+√2 cos ß.

Пп

Ans. (2n+1)π, or +(-1)"
3

35. a(cos 20-1)+2b (cos +1)=0.

π

12

Ans. (2n+1), or cos-1a-b

a

36. Solve

m sin (0+x) = a cos ß, and m cos (0 — x) = a sin ß, for m sin x and m cos x. (Art. 67.)

37. Solve m cos (+ $) = 3.79, and m cos(0 − p) = 2.06,

for m and 0, when

38. Solve

for

r, p, 0. (Art. 70.)

41. Solve cos(2x+3y) = 1, cos (3x+2y)=√3.

Ans. x = nπ ± ± π, y = z nπ ± } π ± 15. 42. Solve cos 30+ cos 50+ √2 (cos + sin 0) cos 0 = Ө 0. Ans. 400= 2nπ ± 3π, or †(2n+1)π.

43. Solve cos 30+ sin 30:

= cos 0+ sin 0.

Ans. sin 0=0, or tan 0

-1±√2.

44. Solve 3 sin 0 + cos 0=2x, sin 0+2 cos 0 = x.

45. Solve 1.268 sin = 0.948 + m sin (25° 27'.2),

1.268 cos = 0.281 + m cos (25° 27'.2).

46. Transform x+y+z1-2yz2-2z2x2 - 2x2y into a Ans. (x+y+z) (y+z−x) (z+x—y)(x+y—z).

product.

47. Eliminate from the equations

m sin 2 0 = n sin 0, p cos 20

=

= q cos 0.

Ans. m2 + p2= n2 + q2.

48. Eliminate and from the equations

x = a cosTM 0 cos" 4, y = b cos" 0 sin" p, z= c sinTM 0.

a tan +b sec 0 = c, a' cot 0 + b' cosec 0 = c'.

Ans. (a'b + cb')2 +(ab' + c'b)2 = (cc' — aa')2.

x = a cos 0 + b cos 2 0, and y = a sin 0 + b sin 2 0.

Ans. a2 [(x+b)2 + y2] = [x2 + y2 — b2]2.

53. Eliminate a and ẞ from the equations

b+c cos au cos (α — 0),

b+c cos B = u cos (ẞ — 0), « — ß=2&;

and show that

u2 - 2 uc cos 0 + c2 = b2 sec2 p.