Question

Find the value of cos^2 π/7 + cos^2 5π/14 + cos^2 8π/7 +cos^2 9π/14 ​

Answer 1

$\huge\mathcal\color{teal} Solution :-$

cos² π/7 + cos² 5π/14 + cos² 8π/7

+ cos² 9π/14

= cos² π/7 + { cos (π/2 -π/7)}²

+ { cos ( π/2 +π/7)}²

= cos² π/7 +sin²π/7 +cos² π/7 +sin²π/7

= 2

Formula :-

☞ sin² ⌀ + cos² ⌀= 1

Answer 2

Answer:

Solution

cos² π/7 + cos² 5π/14 + cos² 8π/7

+ cos² 9π/14

= cos² π/7 + { cos (π/2 -π/7)}²

+ { cos ( π/2 +π/7)}²

= cos² π/7 +sin²π/7 +cos² π/7 +sin²π/7

= 2

Formula :-

☞ sin² ⌀ + cos² ⌀= 1