Conditional Trigonometric Identities
Exercise 5. 4
1. (a) Define conditional trigonometric identities with example.
Solution:
The trigonometric identities which are true only under certain conditions are known as conditional trigonometric identities. Examples of conditional identities are:
(i) If then
(ii) If then
(iii) If then
1. (b) What is the true condition for the identity ?
Solution:
is true, only when
1. (c) Write any three relations which can be formed from
Solution:
Any three relations that can be formed from are
2. (a) If , prove that:
Solution:
2. (b) If , prove that:
Solution:
2. (c) If , prove that:
Solution:
2. (d) If , prove that:
Solution:
2. (e) If , prove that:
Solution:
3. (a) If are the vertices of then prove that:
Solution:
3. (b) If are the vertices of then prove that:
Solution:
3. (c) If are the vertices of then prove that:
Solution:
3. (d) If are the vertices of then prove that:
Solution:
3. (e) If are the vertices of then prove that:
Solution:
4. (a) If , prove that:
Solution:
4. (b) If , prove that:
Solution:
4. (c) If , prove that:
Solution:
4. (d) If , prove that:
Solution:
4. (e) If , prove that:
Solution:
5. (a) If , prove that:
Solution:
5. (b) If , prove that:
Solution:
5. (c) If , prove that:
Solution:
5. (d) If , prove that:
Solution:
6. (a) If , prove that:
6. (b) If , prove that:
6. (c) If , prove that:
6. (d) If , prove that:
6. (e) If , prove that:
Solution:
7. (a) If , prove that:
Solution:
7. (b) If , prove that:
Solution:
7. (c) If , prove that:
Solution:
7. (d) If , prove that:
Solution:
8. (a) If , prove that:
Solution:
8. (b) If , prove that:
Solution:
8. (c) If , prove that:
Solution:
8. (d) If , prove that:
Solution:
9. (a) If , prove that:
Solution:
9. (b) If , prove that:
Solution:
10. (a) If , prove that:
Solution:
Solution:
10. (b) If , prove that:
Solution:
10. (c) If , prove that:
Solution:
10. (d) If , prove that:
Solution:
The End