Trigonometric Identities of Sum and Difference of Angles

Maths, HSSC-KPK First Year. This chapter is split into 48 topics and has 1,157 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Expressing a sin theta + b cos theta as r sin(theta + phi): the angle phi 24 questions
2. Deductions from the fundamental law 21 questions
3. Expressing a sin theta + b cos theta as r sin(theta + phi): the value of r 24 questions
4. Review Exercise 10: recomputed answers 22 questions
5. Tangent of a sum or difference from given tangents 24 questions
6. Allied angles with 3pi/2 and 2pi 24 questions
7. Writing a sine expansion as a single sine 24 questions
8. Exact values of products of sines and cosines 24 questions
9. Converting products into sums or differences 28 questions
10. Exact values of sine of 15 deg multiples 26 questions
11. Exact values using double angle formulas 24 questions
12. Reducing powers of sine and cosine with multiple angles 20 questions
13. Identities for the angles of a triangle 22 questions
14. Exact values of sums and differences of sines and cosines 24 questions
15. Allied angles with pi/2 and pi 24 questions
16. Allied angles and the quadrant rule 21 questions
17. Exact values of trigonometric ratios using allied angles 26 questions
18. Compound angles from given sines and cosines (acute angles) 28 questions
19. Exact values using half angle formulas 26 questions
20. Compound-angle identities from the exercises 26 questions
21. Sum-to-product formulas: recognition and derivation 21 questions
22. Allied angles of cot, sec and cosec 24 questions
23. Simplifying expressions with double angle identities 23 questions
24. Double angle values from tan theta and the quadrant (Example 8) 28 questions
25. Half angle values from cos theta and the quadrant 24 questions
26. Quadrant of the sum or difference of two acute angles 23 questions
27. Proving identities with sum-to-product formulas 26 questions
28. Product-to-sum formulas: recognition and derivation 20 questions
29. Triple angle formulas: recognition and derivation 20 questions
30. Exact values of compound-angle expressions (Example 2) 28 questions
31. Converting sums or differences into products 28 questions
32. Expansion of tan(A +/- B) 24 questions
33. Worked results for a sin theta + b cos theta 21 questions
34. Exact values of cosine of 15 deg multiples 26 questions
35. Compound angles with angles in different quadrants 26 questions
36. Products of cosines and sines at special angles 21 questions
37. Simplifying sums of allied-angle terms 24 questions
38. Triple angle values from given ratios 26 questions
39. Fundamental law of trigonometry and its proof 22 questions
40. Allied-angle relations for the angles of a triangle 28 questions
41. Double angle formulas: recognition and derivation 21 questions
42. Expansion of cos(A +/- B) 24 questions
43. Half angle formulas: recognition and signs 22 questions
44. Exact values of tangent of 15 deg multiples 26 questions
45. Writing a tangent expansion as a single tangent 25 questions
46. Expansion of sin(A +/- B) 24 questions
47. Double angle values from sin theta or cos theta 26 questions
48. Writing a cosine expansion as a single cosine 24 questions