find the value of cos pi/11+cos 3pi/11+cos 5pi/11+cos 7pi/11+cos 9pi/11
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Answer:
Answer: (2) 1/2
Solution:
cos π/11 + cos 3π/11 + cos 5π/11 + cos 7π/11 + cos 9π/11
Multiplying and dividing by 2 sin π/11,
= [2 sin π/11 cos π/11 + 2 sin π/11 cos 3π/11 + 2 sin π/11 cos 5π/11 + 2 sin π/11 cos 7π/11 + 2 sin π/11 cos 9π/11]/ (2 sin π/11)
= [sin 2π/11 + sin 4π/11 – sin 2π/11 + sin 6π/11 – sin 4π/11 + sin 8π/11 – sin 6π/11 + sin 10π/11]/ (2 sin π/11)
= (sin 10π/11)/ (2 sin π/11)
= [sin(π – π/11)]/ (2 sin π/11)
= 1/2
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