. 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). . 11. cos x + cosy = 2 cos } (x + y) cos(x - y). 12. cosy - cos x=2 sin }(x + y) sin (2 - y). 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. 24. cos2x = cos? x – sino x =1- 2 sinox 2 sin a 25. 1 - cos 2 x = tan’x. 2 cos2x 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 13. Simplify 2 cos 20 cos 0 - 2 sin 46 sin 6. Ans. 2 cos 30 cos 2 . 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. 35. sin no cos 0 + cos no sin 0= sin (n + 1) 0. tan (n + 1) – tan ng 39. tan p. |