Question

If pi/13 = alpha so prove that cos 3 alpha + cos 5 alpha +2 cos alpha cos 9 alpha = 0​

Answer 1

Answer:

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.

Step-by-step explanation:

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