Question

971 376 5л
2 cos COS —+cos
+ cos — + cos - =0
13 13 13 13​

Answer 1

Explanation:

L.H.S.

2cos

13

π

cos

13

9π

+cos

13

3π

+cos

13

5π

Using that,

2cosAcosB=cos(A+B)+cos(A−B)

2cos

13

π

cos

13

9π

+cos

13

3π

+cos

13

5π

=cos(

13

π

+

13

9π

)+cos(

13

π

−

13

9π

)+cos

13

3π

+cos

13

5π

=cos

13

10π

+cos(−

13

8π

)+cos

13

3π

+cos

13

5π

∴cos(−θ)=cosθ

=cos

13

10π

+cos

13

8π

+cos

13

3π

+cos

13

5π

=cos(π−

13

3π

)+cos(π−

13

5π

)+cos

13

3π

+cos

13

5π

=−cos

13

3π

−cos

13

5π

+cos

13

3π

+cos

13

5π

=0

R.H.S

Hence, proved.