NCERT Class XI Mathematics - Trigonometric Functions - Solutions | Question 52

NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 52

Total: 61

2 cos

π

13

cos

9π

13

+ cos

3π

13

+ cos

5π

13

= 0

Solution:

We have,
L.H.S. = 2 cos

π

13

cos

9π

13

+ cos

3π

13

+ cos

5π

13

= cos (

9π

13

+

π

13

) + cos (

9π

13

−

π

13

) + cos

3π

13

+ cos

5π

13

= cos

10π

13

+ cos

8π

13

+ cos

3π

13

+ cos

5π

13

= cos (

13π−3π

13

) + cos (

13π−5π

13

) + cos

3π

13

+ cos

5π

13

= - cos

3π

13

- cos (

5π

13

) + cos

3π

13

+ cos

5π

13

Since cos (π - θ) = - cos θ
= 0 = R.H.S.

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