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61. Table of Useful Formulæ. The following is a list of important formulæ proved in this chapter, and summed up for the convenience of the student: 1. sin (x + y)

sin x cos y + cos x siny . (Art. 43) 2. cos (x + y) = cos x cos Y - sin x siny.

3. sin (2 y) = sin x cosy – cos a siny (Art. 44) (4. cos (x - y) = cos x cos y + sin x siny. 5. 2 sin x cos y = sin (x+y)+sin (- y)

2 (Art. 45) 6. 2 cosa siny = sin(x + y) - sin (x - y). 7. 2 cos x cos y = cos (x + y) + cos (x – y). 8. 2 sin x siny = cos (ac y) - cos (x + y). 9. sin x + siny=2 sin }(x + y) cos } (x y). 10. sin x - siny=2 cos(x + y) sin } (x - y).

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11. cos x + cosy = 2 cos } (x + y) cos(x - y).

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12. cosy - cos x=2 sin }(x + y) sin (2 - y).

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19. sin (x+y) sin (2 y)=sinox – sino y = cos” y cosé 2.

20. cos (x+y) cos (x y) = cosé x — sin’y=cos’y — sinox.

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24. cos2x = cos? x – sino x =1- 2 sinox

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2 sin a

25.

1 - cos 2 x
1 + cos2x

= tan’x. 2 cos2x

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3 3. If cos (=

4 and sin (Q B).

and cos B =, find a value for sin («+B),

, 2 V7+3 V21 2 V7 – 3 V21 Ans. 20

20

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13. Simplify 2 cos 20 cos 0 - 2 sin 46 sin 6.

Ans. 2 cos 30 cos 2 .

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21. cos (60° + A) + cos (60° – A)= cos A.

22. cos (45° + A) + cos (45o - A)= V2cos A.

23. sin (45°+ A) – sin (45° — A) = V2 sin A.

24. cos 20 + cos 40 = 2 cos 3 0 cos 0.

25. cos 40 - cos 60 = 2 sin 5 A sin 0.

26. cos 0 + cos 30 + cos 5 0 + cos 70 = 4 cos cos 20 cos 40.

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35. sin no cos 0 + cos no sin 0= sin (n + 1) 0.

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tan (n + 1) – tan ng
1 + tan (n + 1) $ tan ng

39.

tan p.

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