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· Cos 10° + cos 110° + cos 130° |
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Answer» cos 10 + cos 110 + cos 130 = (cos 10 + cos 110) + cos 130 = 2 cos (110 + 10)/2 * cos (110 - 10)/2 + cos 130 {using cos C + cos D = 2 cos (C + D)/2 * cos (C - D)/2 } = 2 cos 120/2 * cos 100/2 + cos (180 - 50) ( As 130 = 180 - 50) = 2 cos 60 * cos 50 - cos 50 (Using cos (180 - A) = - cos A) = 2 * 1/2 * cos 50 - cos 50 ( As cos 60 = 1/2) = cos 50 - cos 50 = 0 |
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