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sin2pi/7+sin4pi/7+sin8pi/7=

sin2pi/7+sin4pi/7+sin8pi/7=

Grade:12th pass

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
6 years ago
Hello student, Please find the answer to your question below

sin2pi/7+sin4pi/7+sin8pi/7=

Let 2pi/7 = x
so equation becomes
sin x + sin 2x + sin 4x
[use the following formula sin x + sin 2x + sin 4x + sin 8x + ….. n terms= sin (2^n x ) / 2* sin x ]
= sin 8x / 8 * sin x
= sin (16pi/7) / 8*sin(2pi/7)
= 1/8 [because sin (16pi/7) = sin (2pi /7 )]

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