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Ex 7.3, 13 - Integrate cos 2x - cos 2a / cos x - cos a - Ex 7.3

Ex 7.3, 13 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.3, 13 Integrate the function cosโกใ€–2๐‘ฅ โˆ’ cosโก2๐›ผ ใ€—/cosโกใ€–๐‘ฅ โˆ’ cosโก๐›ผ ใ€— โˆซ1โ–’ใ€–cosโกใ€–2๐‘ฅ โˆ’ cosโก2๐›ผ ใ€—/cosโกใ€–๐‘ฅ โˆ’ cosโก๐›ผ ใ€— " " ๐‘‘๐‘ฅใ€— =โˆซ1โ–’((2 cos^2โกใ€–๐‘ฅ โˆ’ 1ใ€— ) โˆ’ (2 cos^2โกใ€–๐›ผ โˆ’ 1ใ€— ))/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =โˆซ1โ–’(2 cos^2โกใ€–๐‘ฅ โˆ’ 1ใ€— โˆ’ 2 cos^2โกใ€–๐›ผ + 1ใ€—)/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =โˆซ1โ–’(2 cos^2โก๐‘ฅ โˆ’ 2 cos^2โก๐›ผ + 1 โˆ’ 1)/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =โˆซ1โ–’2(cos^2โก๐‘ฅ โˆ’ cos^2โก๐›ผ )/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =2โˆซ1โ–’(cos^2โก๐‘ฅ โˆ’ cos^2โก๐›ผ)/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =2โˆซ1โ–’((๐‘๐‘œ๐‘ โก๐‘ฅ โˆ’ ๐‘๐‘œ๐‘ โก๐›ผ ) (๐‘๐‘œ๐‘ โก๐‘ฅ + ๐‘๐‘œ๐‘ โก๐›ผ ))/((๐‘๐‘œ๐‘ โก๐‘ฅ โˆ’ ๐‘๐‘œ๐‘ โก๐›ผ ) ) ๐‘‘๐‘ฅ =2โˆซ1โ–’(๐‘๐‘œ๐‘ โก๐‘ฅ+๐‘๐‘œ๐‘ โก๐›ผ ) ๐‘‘๐‘ฅ =2(โˆซ1โ–’๐‘๐‘œ๐‘ โก๐‘ฅ ๐‘‘๐‘ฅ+โˆซ1โ–’๐‘๐‘œ๐‘ โก๐›ผ ๐‘‘๐‘ฅ) =2(โˆซ1โ–’๐‘๐‘œ๐‘ โก๐‘ฅ ๐‘‘๐‘ฅ+๐‘๐‘œ๐‘ โก๐›ผ โˆซ1โ–’1. ๐‘‘๐‘ฅ) =๐Ÿ(๐’”๐’Š๐’โก๐’™+๐’™โก๐’„๐’๐’” ๐œถ)" +" ๐‘ช (๐‘๐‘œ๐‘ โก2๐œƒ=2 ใ€–๐‘๐‘œ๐‘ ใ€—^2โก๐œƒโˆ’1)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.