Expand eacf of the following:

1. sin(2x - y) 2. cos(q - 2a) 3. sin(3A + 4B)

4. cos(2P + 5Q) 5. sin(A + 45) 6. cos(A + p/3)

7. tan(A + 3B) 8. tan(2X - Y) 9. tan(a + p/4)

10. tan(3p/4 - b)

Simplify each of the following expressions

11. cosA.cos2B - sinA.sin2B 12. sin2a.cosb - cos2a.sinb

13. sin10.cos20 + cos10.sin20 14.

15. 16.

17. cos(A+B).cosB + sin(A+B).sinB 18. sin(q-a).cosq - cos(q-a).sinq

19. sin(2A+B-C).cos(A-B+C) + cos(2A+B-C).sin(A-B+C)

20.

21. sin(A+B).sin(A-B) - cos(A+B).cos(A-B)

Show that

22. sin(45+q) - sin(45-q) = sinq 23. cos(p/3 + q) + sin(p/6 + q) = cosq

24. sin(A+B) + sin(A-B) = 2sinA.cosB 25. cos(a-b) - cos(a+b) = 2sina.sinb

26. 27.

28. 29.

30. (a) If cosx.cosy = and sinx.siny = , find the least positive value of (x + y) and (x - y).

(b) Prove that

(c) Prove that

ANSWERS:

1. sin2x.cosy-cos2x.siny 2. cosq.cos2a+sinq.sin2a 3. sin3A.cos4B+cos3A.sin4B

4. cos2P.cos5Q-sin2P.sin5Q 5. 6.

7. 8. 9. 10. 11. cos(A+2B)

12. sin(2a-b) 13. 1/2 14. 1/ 15. 1 16. tan(4B) 17. cosA 18. -sina 19. sin3A

20. cosa 21. -cos(2A).