Question

Cos 40º + Cos 80º + Cos 160º + Cos 240º =

a) 0 b) 1 c) 1/2 d) -1/2

Answer the option​

Answer 1

Answer:

I think the answer is 1 or 0

Answer 2

Step-by-step explanation:

Correct option is

D

−1/2

cos 40 + cos 80 + cos 160 + cos 240

=2cos(

2

40+80

)cos(

2

40−80

)+cos(180−20)+cos(180+60)

=2cos60.cos(−20)+(−cos20)+(−cos60)

∵cosC+cosD=2cos(

2

C+D

).cos(

2

C−D

)

cos(180+θ)=−cosθ

cos(180−θ)=−cosθ

=2×

2

1

cos(20)−cos(20)−

2

1

(cos(−θ)=cosθ)

=cos20−cos20−

2

1

=−

2

1