Plane trigonometry, by S.L. Loney.

124 TRIGONOMETRY. [Exs. XVIII.]
8. If sin 0 + sin = a and cos + cos =b, find the value of tan 8-2
Prove that
9. (cosa+cos )2 +(sin a -sinp)2=4 cos2.
10. (cosa cos ) (si)2 + ( sin a si)2= 4 cos22.
11. (cos a - cos)2 + (sin a - sin )2=44 sin2-
A
2 tan A 1 - tan2
2 2
12. sinA =. 13. cos = -.
1 + tan2 I + tan2
2 2
14. sec ( + 0) sec - =2 sec 20.
15.1 + sin A
15. tan (45~+- s2 == sec A + taan A.
16. i2Asin 2 A A ) A
17. cos2 a + cos2 (a +120~) + cos2 (a - 120~) =.. 3w1 57 77r 3
18. cos4 +cos4 - + cos4 + cos4 8 - = 3
8 8 8 8-2'
19. sin4 8 + sin4 3 sin 5 + sin4 7r = 3
8 98 8 82'
20. cos 28 cos 2q + sin2 ( - ) - sin2 ( + 0)= cos (20 + 20).
21. (tan 4A + tan 2A) (1- tan2 3Atan2A) =2tan3A sec2 A.
22. 1+tan -see (1 +tan 2 + sec =sin a sec2.
Find the proper signs to be applied to the radicals in the 3 following
formulae.
A A
23. 2 cos a = 1 - sin A - N/1 + sin A, when 2 = 278~.
24. 2 sin = /1 - sin A A ^/1 + sin A, when -1 -2 2 11