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Adding (4) and (5), we have

C2
a + b + = 1.

sin'e

= d.

cos A.

=

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5. Eliminate from the equations

a sin $ + bcos $ = C,

a cos $ – b sind Ans. a? +62 = + do. 6. Eliminate 0 from the equations m = cosec

sin 0, n = sec A

mini (mi + n3)=1. 7. Eliminate 0 and $ from the equations

sin 0 + sin •
cos 0 + cos d=b,
cos(0-0)=c.

a? +62-2c=2. 8. Eliminate x and y from the equations

tan x + tany = 0,
cot x + coty=b,

1 1 x+y=C.

cotc=

b 9. Eliminate from the equations

X = cos 2€ + cos ,
y=sin 20 + sin d.

Ans. 2x=(x2 + y) - 3(2x + yo).

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a

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4. 2 sine + V2 sin A= 2.

45o.

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13. (cot 6 – tan 6)?(2 +V3)=4(2-V3).

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14. cosec 0 cot 0 = 2V3.

2 na £

6

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22. Solve m sin =1.29743, and m cos 0 = 6.0024.

Ans. ($<180°).

23. Solve m sin ø= -0.3076258, and m cos p=0.4278735. (m positive.)

Ans. ø= 324° 17' 6".6, m = 0.52698. 24. Solve m sin $ 0.08219, and m cos = 0.1288.

25. Solve m sin ♡

194.683, and mcos $

= 8460.7.

26. If a sin 0 + b cos 0 =c, and a cos 0 + b sin 0=csin cos e, show that sin 2 0(c? a62) = 2 ab.

Solve the following equations :

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4

27. V2 sin + V2 cos 6 = V3. Ans. – +na+(-1)"} 0 0

nT -).

3 28. 2 sin x + 5 cos x = 2. Sug. [2.5 = tan 68° 12'].

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

X

29. 3 cos x — 8 sin x = : 3. Sug. [2.6 = tan 69° 26' 30"].

Ans. x=-69° 26' 30" + 2 n 180° + (69° 26'30").

30. 4 sin a

- 15 cos x = 4. Sug. [3.75 = tan 75° 4'].

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

31. cos(a + x)=sin(« + x) + V2 cos ß.

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32. cos 0 + cos 30 + cos 5 0 = 0.

Ans. (2n + 1), or }(3 n + 1).

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33. sin 50 = sin 30 + sin 0 = 3 – 4 sino 0.

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34. 2 sin’30 + sino 66=2.

Ans. ](2n +1), or "* +(-1)" 12

. ) 35. a(cos 2 0 – 1) + 2 b(cos @ +1)= 0.

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

a

36. Solve

m sin(8 + x) = a cos B, and m cos (0 — x)= a sin ß, for m sin x and m cos x. (Art. 67.)

Ans. m sin x=

a cos(B+A)

cos 20 a sin(B 6).

cos 20 37. Solve m cos(+ )=3.79, and m cos(0 - )=2.06, for m and 0, when p=31° 27'.4. (Art. 67.)

,

m cOS X =

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41. Solve cos (2x + 3y)= i, cos (3x + 2y)= įV3.

Ans. = nt *5, y=kna +} 15 T.

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42. Solve cos 30 + cos 5 0 +V2(cos 0 + sin 6)cos 0 = 0.

Ans. 40+0= 2n1 + $T, or 1(2n + 1).

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43. Solve cos 30 + sin 30= cos 0 + sin 0.

Ans. sin ( = 0, or tan (=-1+ V2.

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

Ans. 0 = 71° 34', x= 1V10. 45. Solve 1.268 sin ø= 0.948 + m sin(25° 27'.2), 1.268 cos p=0.281 + m cos (25° 27'.2).

Ans. 0= 60° 53'.8, m=0.372. 46. Transformat + y + 34 - 2 yoz2 – 2 z*.x2 – 2 xạya into a product. Ans. — (x+y+z) (y+--2)(2+x-Y) (x+y-2). 47. Eliminate 0 from the equations m sin 20=n sin 0, p cos 20= q cos 0.

Ans. m2 + pé = n2 + q*. 48. Eliminate and from the equations x = a cosm 0 cos” , y=b cos” 0 sin" , 2= c sin" 0.

Ans.

y
m+

.

m

m

m

m

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=

49. Eliminate from the equations
a sin 0 + b cos 0 = h, a cos 0 b sin 0=k.

Ans. a? +1=h+ . 50. Eliminate 0 from the equations a tan 0 + b sec 0=c, a' cot 0 + cosec 0 = c.

Ans. (a'b + cb')2 + (ab' + c'b)2 = (cc' aa')? 51. Eliminate 0 from the equations

x = 2 a cos A cos 2 0 a cos 0,

y= 2 a cos o sin 20 a sin 0. Ans. x2 + y2 = a?. 52. Eliminate from the equations x = a cos 0 + b cos 20, and y= a sin 0 + b sin 20.

Ans. a [(x +b)” + y']=[x2 + y2 b?]?.

53. Eliminate a and B from the equations

b + c cosa = u cos (« 0),

b + c cos ß = u cos (B 0), « B= 20; and show that

u2 uc cos 0 + c2 = b2 sec? d.

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