Question

If a = 2pi/7 then which of the following is/are true?
(A) cos a + cos 2a + ... + cos 6a = 0
(B) sin a + sin 2a + ... + sin 6a = 0
(C) sin a + sin 2a + sin 4a = 77/2
(D) sin, sin a sin q = 77/8​

Answer 1

Answer

Correct option is

A

0

sin  

6

A+cos  

6

A+3sin  

2

Acos  

2

A−1=(sin  

2

A+cos  

2

A)(sin  

4

A−sin  

2

Acos  

2

A+cos  

4

A+3sin  

2

Acos  

2

A−1)

=1×(sin  

4

A+2sin  

2

Acos  

2

A+cos  

4

A)−1

=(sin  

2

A+cos  

2

A)  

2

−1

=(1)  

2

−1=1−1=0

Hence answer is zero (0)