Ex 2.2, 19 - Find cos-1(cos 7pi/6) is equal to (A) 7pi/6 - Finding pricipal value

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Ex 2.2, 19 Find the values of cos-1(cos 7ฯ€/6) is equal to (A) 7ฯ€/6 (B) 5๐œ‹/6 (C) ๐œ‹/3 (D) ๐œ‹/6 Let y = cos โˆ’1 (cos 7ฯ€/6) cos y = cos (7ฯ€/6) cos y = cos (210ยฐ) We know that range of principal value of cos is [0,ฯ€] i.e. [0ยฐ ,180ยฐ] Hence y = 210ยฐ not possible Now, cos y = cos (210ยฐ) cos y = cos (360ยฐ โ€“ 150ยฐ) cos y = cos (150ยฐ) cos y = cos (150 ร— ๐œ‹/180) cos y = cos (5๐œ‹/6) y = 5๐œ‹/6 Which is in the range of principal value of cos-1 i.e. [0,ฯ€] Hence , cos โˆ’1 (cos 7ฯ€/6) = y = 5๐œ‹/6 Thus, option (B) is correct

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