Plane trigonometry, by S.L. Loney.

102

TRIGONOMETRY.

EXAMPLES. XVI.
1 1
1. If tanA=- and tanB =, find the values of tan (2A +B) and
tan (2A - B).
2. If tan A = 4, and tan B = prove that
4 -,/3 4+,,/3
tan (A - B)= 375.
3. 1
3. If tanA= n- and tan B= -1 find tan (A + B).
5 1
4. If tan a = and tan p=-, prove that a + =.
Prove that
5. tan + 0)xtan (3 0)=-l.
6. cot 7 + 0 cot 4 - =1.
A A
7. l+tanA tan tan A cot- 1=secA.
2 2
102. As further examples of the use of the formulae
of the present chapter we shall find the general value of
the angle which has a given sine, cosine or tangent. This
has been already found in Arts. 82-84.
Find the general value of all angles having a given sine.
Let a be any angle having the given sine and 0 any
other angle having the same sine.
We have then to find the most general value of 0
which satisfies the equation
sin 0 = sin a,
i.e. sin 0 - sin a = 0.
This may be written
O+a. 0-a
2 cos sin =0,
2 2