Plane trigonometry, by S.L. Loney.

MULTIPLE ANGLES.

109

EXAMPLES. XVII.
1. Find the value of sin 2a when
3 12 16
(1) cosa=, (2) sin a= and (3) tana=-.
2. Find the value of cos 2a, when
15 4 5
(1) cosa=y, (2) sina=5, and (3) tana=-.
3. If tan 0 =-, find the value of a cos 20 + b sin 20.
a
Prove that
sin 2A sin 2A
4. =tanA. 5. =cotA.
1 + cos 2A 1 - cos 2A
1 - cos 2A
6. cos 2A= tan2A. 7. tan A + cot A = 2 cosec 2A.
8. tan A - cot A = - 2 cot 2A. 9. cosec 2A + cot 2A = cot A.
1-cosA+ cos B- cos (A +B) A B
101+osA-osB-cos(A+B) =tan cot
10 + cos A - cos B - cos (A + B) 2 2
cos iA = (tn 45~ - sec 8A-1 tan 8A
1 r.sinA2 12. see 4A-i tan 2A
13. t ( A)cosec 2A.
a+p3
tan2 (45- A)
tan a
14. sin (+3) 2
sin (a+/) t 2
14. sin( ----~fii
2
sin2 A -- sin2 B
15. tan (A + B).
sin A cos A - sin B cos B ta (B).
16. tan +0) -tan - )=2 tan 20.
cosA+sinA cosA-sinA
17.. = 2 tan 2A.
cosA -sin A cos A + sin A
4 cos (A15 tan 15 2A
18. cot (A + 15~) - tan (A - 15~)=- s 2A
1+ 2 sin 2A