Multiple Angles
Multiple Angles
Exercise - 5.1 [ Page - 157 ]
1. (a) Define multiple angle with an example.
Solution:
If A be any angle then 2A, 3A,.... etc are called multiple angles of A.
1. (b) Write in terms of and
Solution:
2. (a) Write in terms of
Solution:
2(b) Write in terms of
Solution:
2(c) Write in terms of .
Solution:
2(d) Write in terms of
Solution:
3.(a) If , find the value of .
Solution:
Given,
Now,
3. (b) If and , then find the value of .
Solution:
Given,
and
We know that,
3(c) If , find the value of .
Solution:
Given
Now,
3(d) , find the value of and .
Solution:
Given,
Now,
Again,
3(e) If , find the value of and
Solution:
And
3. (f) If , find the value of and
Solution:
And
Alternative
Now
And
3. (g) If , find the value of and
Solution:
Now,
And
3. (h) If , find the value of .
Solution:
Given,
Now,
4. (a) If , then show that
Given,
We know that,
4.(b) If , then show that .
Solution:
Given,
We know that,
5. (a) Prove that:
Solution:
First Method:
Second Method:
5. (b) Prove that:
Solution:
First Method:
Second Method:
5. (c) Prove that:
Solution:
5. (d) Prove that:
Solution:
6. (a)
Solution:
6(b)
Solution:
6. (c)
Solution:
6. (d)
Solution:
6. (e)
Solution:
6. (f)
Solution:
6. (g)
Solution:
6. (h)
Solution:
6. (i)
Solution:
6. (j)
Solution:
6. (k)
Solution:
7. (a)
Solution:
7. (b)
Solution:
7. (c)
Solution:
7. (d)
Solution:
7. (e)
Solution
7. (f)
Solution:
8. (a) If then prove that:
Solution:
8. (b) If
Prove that:
8. (c) If , show that
Solution:
Alternative
9. (a)
Solution:
9. (b)
Solution:
10. (a) Prove that:
Solution:
10. (b)
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:
11. (e) Prove that:
Solution:
11. (f) Prove that:
Solution:
12. (a)
Solution:
12. (b)
Soluion:
12. (c) Prove that:
Solution:
12. (d) Prove that:
Solution:
12. (e) Prove that:
Solution:
13. (a) Prove that:
Solution:
13. (b) Prove that:
Solution:
13. (c) Prove that:
Solution:
13. (d) Prove that:
Solution:
14 (i) If prove that
Solution:
Given,
Now,
14 (ii) prove that:
Solution:
Given,
15. (a) Prove that:
Solution:
15. (b) Prove that:
Solution:
15. (c) Prove that:
Solution:
15 (d) Prove that:
Solution:
16. With the help of multiple angles relation of Sine and Cosine, find the value of and . By using these values, find the values of and . Also, find the value of and . Share your result to your friend and prepare combine report.
Solution:
Now, comparing with , we get
Now,
Since is positive,
Now,
Now,
Also,
Also,
Also
Also,
Also,