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Question 5 Solve tan 2x = โ€“ cot (x" + " ๐œ‹/3) tan 2x = โ€“cot (๐‘ฅ" + " ๐œ‹/3) We need to make both in terms of tan Rough tan (90ยฐ + ฮธ) = โ€“cot ฮธ โ€“cot ฮธ = tan (90ยฐ + ฮธ) โ€“cot ฮธ = tan (๐œ‹/2 " + ฮธ" ) Replacing ฮธ by x + ๐œ‹/3 โ€“cot ("x + " ๐œ‹/3) = tan (๐œ‹/2 "+ x +" ๐œ‹/3) tan 2x = tan (๐œ‹/2+x" + " ๐œ‹/3) tan 2x = tan (๐œ‹/2 " + " ๐œ‹/3 " + x" ) tan 2x = tan ((3๐œ‹ + 2๐œ‹)/(2 ร— 3) " + x" ) tan 2x = tan (5๐œ‹/6 " + x" ) General solution Let tan x = tan y tan 2x = tan 2y From (1) and (2) tan 2y = tan (5๐œ‹/6 " + x" ) 2y = 5๐œ‹/6 + x General solution is 2x = nฯ€ + 2y where n โˆˆ Z Put 2y = ("x + " 5๐œ‹/6) 2x = nฯ€ + ("x + " 5๐œ‹/6) 2x โ€“ x = nฯ€ + 5๐œ‹/6 x = nฯ€ + ๐Ÿ“๐…/๐Ÿ” where n โˆˆ Z

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.