Transformation Of Trigonometric Formula
Exercise 5.3
1. (a) Express into the sum or difference of Sine or Cosine.
Solution:
1. (b) Express into the sum or difference of Cosine.
Solution:
1. (c) Reduce into the sum or difference of Cosine.
Solution:
2. (a) Express into the product form of Sine and Cosine.
Solution:
2. (b) Express into the product form of sine.
Solution:
3.(a) If and , find the value of .
Solution:
3.(b) If and , find the value of .
Solution:
4. (a) Find the value of:
Solution:
4. (b) Find the value of:
Solution:
4. (c) Find the value of:
Solution:
4. (d) Find the value of:
Solution:
4. (e) Find the value of:
Solution:
4. (f) Find the value of:
Solution:
5. (a) Express the following product into sum or difference form:
Solution:
5. (b) Express the following product into sum or difference form:
Solution:
5. (c) Express the following product into sum or difference form:
Solution:
5. (d) Express the following product into sum or difference form:
Solution:
5. (e) Express the following product into sum or difference form:
Solution:
5. (f) Express the following product into sum or difference form.:
Solution:
5. (g) Express the following product into sum or difference form:
Solution:
5. (h) Express the following product into sum or difference form:
Solution:
6. (a) Express the following sum or difference into product form.
Solution:
6. (b) Express the following sum or difference into product form.
Solution:
6. (c) Express the following sum or difference into product form.
Solution:
6. (d) Express the following sum or difference into product form.
Solution:
6. (e) Express the following sum or difference into product form.
Solution:
6. (f) Express the following sum or difference into product form.
Solution:
7. (a) Prove that:
Solution:
7. (b)
Solution:
7(c)
Solution:
7. (d)
Solution:
7. (e)
Solution:
7. (f)
Solution:
7. (g)
Solution:
7. (h)
Solution:
8. (a)
Solution:
8. (b)
Solution:
8. (c) Prove that:
Solution:
8. (d) Prove that:
Solution:
8. (e) Prove that:
Solution:
8. (f) Prove that:
Solution:
9. (a) Prove that:
Solution:
10. (d) Prove that:
Solution:
10. (e) Prove that:
Solution:
10. (f) Prove that:
Solution:
10. (g) Prove that:
Solution:
11. (a) Prove that:
Solution:
11. (b) Prove that:
Solution:
11. (c) Prove that:
Solution:
11. (d) Prove that:
Solution:
12. (a) Prove that:
Solution:
12. (b) Prove that:
Solution:
12. (c) Prove that:
Solution:
12. (d) Prove that:
Solution:
13. (a) Prove that:
Solution:
13. (b) Prove that:
Solution:
13. (c) Prove that:
Solution:
13. (d) Prove that:
Solution:
13. (e) Prove that:
Solution:
13. (f) Prove that:
Solution:
13. (g) Prove that:
Solution:
13. (h) Prove that:
Solution:
14. (a) Prove that:
Solution:
14. (b) Prove that:
Solution:
14. (c) Prove that:
Solution:
14. (d) Prove that:
Solution:
15. (a) Prove that:
Solution:
15. (b) Prove that:
Solution:
Alternative,
Solution:
15. (c) Prove that:
Solution:
15. (d) Prove that:
Solution:
16. (a)
Solution:
Given,
Now,
16. (b)
Solution:
1. (a) Express into the sum or difference of Sine or Cosine.
Solution:
1. (b) Express into the sum or difference of Cosine.
Solution:
1. (c) Reduce into the sum or difference of Cosine.
Solution:
2. (a) Express into the product form of Sine and Cosine.
Solution:
2. (b) Express into the product form of sine.
Solution:
3.(a) If and , find the value of .
Solution:
3.(b) If and , find the value of .
Solution:
4. (a) Find the value of:
Solution:
4. (b) Find the value of:
Solution:
4. (c) Find the value of:
Solution:
4. (d) Find the value of:
Solution:
4. (e) Find the value of:
Solution:
4. (f) Find the value of:
Solution:
5. (a) Express the following product into sum or difference form:
Solution:
5. (b) Express the following product into sum or difference form:
Solution:
5. (c) Express the following product into sum or difference form:
Solution:
5. (d) Express the following product into sum or difference form:
Solution:
5. (e) Express the following product into sum or difference form:
Solution:
5. (f) Express the following product into sum or difference form.:
Solution:
5. (g) Express the following product into sum or difference form:
Solution:
5. (h) Express the following product into sum or difference form:
Solution:
6. (a) Express the following sum or difference into product form.
Solution:
6. (b) Express the following sum or difference into product form.
Solution:
6. (c) Express the following sum or difference into product form.
Solution:
6. (d) Express the following sum or difference into product form.
Solution:
6. (e) Express the following sum or difference into product form.
Solution:
6. (f) Express the following sum or difference into product form.
Solution:
7. (a) Prove that:
Solution:
7. (b)
Solution:
7(c)
Solution:
7. (d)
Solution:
7. (e)
Solution:
7. (f)
Solution:
7. (g)
Solution:
7. (h)
Solution:
8. (a)
Solution:
8. (b)
Solution:
8. (c) Prove that:
Solution:
8. (d) Prove that:
Solution:
8. (e) Prove that:
Solution:
8. (f) Prove that:
Solution:
9. (a) Prove that:
Solution:
10. (d) Prove that:
Solution:
10. (e) Prove that:
Solution:
10. (f) Prove that:
Solution:
10. (g) Prove that:
Solution:
11. (a) Prove that:
Solution:
11. (b) Prove that:
Solution:
11. (c) Prove that:
Solution:
11. (d) Prove that:
Solution:
12. (a) Prove that:
Solution:
12. (b) Prove that:
Solution:
12. (c) Prove that:
Solution:
12. (d) Prove that:
Solution:
13. (a) Prove that:
Solution:
13. (b) Prove that:
Solution:
13. (c) Prove that:
Solution:
13. (d) Prove that:
Solution:
13. (e) Prove that:
Solution:
13. (f) Prove that:
Solution:
13. (g) Prove that:
Solution:
13. (h) Prove that:
Solution:
14. (a) Prove that:
Solution:
14. (b) Prove that:
Solution:
14. (c) Prove that:
Solution:
14. (d) Prove that:
Solution:
15. (a) Prove that:
Solution:
15. (b) Prove that:
Solution:
Alternative,
Solution:
15. (c) Prove that:
Solution:
15. (d) Prove that:
Solution:
16. (a)
Solution:
Given,
Now,
16. (b)
Solution: