Sub-Multiple Angles [CDC]
Exercise 5. 2 [ Page 167 ]
1. (a) Define submultiple angle with an example.
Solution:
If be any angle, then etc. are called sub-multiple angles of A.
1. (b) Write in terms of
Solution:
1. (c) Write in terms of and in terms of .
Solution:
2. (a) If and , find the value of .
Solution:
Given, and
Now,
2 (b) If find the value of .
Solution:
2. (c) If , find the value of .
Solution:
3. (a) If , find the value of and .
Solution:
Given,
Now,
Also,
Also,
3. (b) If , find the value of and .
Solution:
Also,
Also,
3. (c) If , find the value of and .
Solution:
Given,
4. (a) If , find the value of and .
Solution:
Given,
Again,
4. (b) If , find the value of .
Solution:
Given,
Now,
4. (c) If , find the value of .
Solution:
Given,
Now,
5. (a) If , show that, .
Solution:
5. (b) If , prove that .
Solution:
5. (c) If show that:
Solution:
Alternative
5. (d) If , prove that:
Solution:
Alternative
6. (a) If , prove that:
and
Solution:
6(b) If show that:
(i)
(ii)
(iii)
Solution:
7. (a) Prove that:
Solution:
7. (b) Prove that:
Solution:
7. (c)
Solution:
7. (d)
Solution:
7 (e)
Solution:
7 (f)
Solution:
7. (g) Prove that:
Solution:
7. (i) Prove that:
Solution:
7. (j)
Solution:
7. (k) Prove that:
Solution:
7. (l) Prove that:
Solution:
7. (m) Prove that:
Solution:
8. (a) Prove that:
Solution:
8. (b) Prove that:
Solution:
8. (c) Prove that:
Solution:
8. (d) Prove that:
Solution:
9. (a) Prove that:
Solution:
9. (b) Prove that:
Solution:
10. (a) Prove that:
Solution:
10. (b) Prove that:
Solution:
10. (c) Prove that:
Solution:
10. (d)
Solution:
11. (a) Prove that: Solution:
11. (b) Prove that:
Solution:
11. (c) Prove that:
Solution:
11. d) Prove that:
Solution:
12. If then prove that:
Solution:
Given,