Plane trigonometry, by S.L. Loney.

338

TRIGONOMETRY.

[Exs. L.]

1 sin o e0 -e 2]
21. 34L - 20 2

sin2 /vmn 0 - sinmr sin nO
22. -cosm -cos
(1 - cos mo) (1 - cos nO) '

3 sin x - sin 3x
23 *
- sin x
n -sin 2 sin + (1- cos )3
24. -
sin x sin 2x - 8 cos x sin2 --- sin4 x
2 3

ax - bx
25..
X

3
26. (tan x)2
x

m

27. cos -+ sin.3
m mJ
Find the value, when x equals, of
28. (cos x + sin 2x + cos 3x)2
(sinx + 2cos 2x- sin 3x)3'
tan 0
29. (sin )n. 30. sec- tan
Find the value, when n is infinite, of
31. cos -. 32. (cos -)

X.

33. (cos n.
1

34. If n be >1 and 0==7 nearly, prove that (sin 0) is very nearly
equal to
(n- 1) + (n+ 1) sin
(n+ 1) +(n-l) sin O'
35. In the limit, when /3=a, prove that
a sin /3 - p sin a
= tan (a - tan-! a).
a cos / - P Cos a
36. Prove that
4tan-' - _=1tan-
4 tan-1 -= tan-9
5 4 239
and deduce that in a triangle ABC, in which C is a right angle and CA is
five times CB, the angle A exceeds the eighth part of a right angle by
3' 36", correct t6o the nearest second.