Question

The value of cos10+Cos20+Cos30+.........+cos360=

Answer 1

Answer:

The sum of values cos10+cos20+............ +cos360=0

Answer 2

Answer:

The value of cos(10°)+Cos(20°)+Cos(30°)+.........+cos(360°)= O

Explanation:

We know that cos (180 + Ф) = -cosФ

Therefore by applying this formula in the equation cos(10°)+Cos(20°)+Cos(30°)+.........+cos(360°)

We get,

= cos (10°) + cos (20°) + cos (30°) + cos (40°) + ... + cos (180°)+ cos (180+10°) + cos (180+20°) + cos (180+30°)+ ...... + cos (180+180°)

= cos (10°) + cos (20°) + cos (30°) + cos (40°) + ... + cos (180°) -cos (10°) - cos (20°) - cos (30°) - cos (40°) - ... - cos (180°)

= 0

Hence, cos(10°)+Cos(20°)+Cos(30°)+.........+cos(360°)= O

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