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Ex 7.3, 8 - Integrate 1 - cos x / 1 + cos x - Integration using trigo identities - 2x formulae

Ex 7.3, 8 - Chapter 7 Class 12 Integrals - Part 2

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Transcript

Ex 7.3, 8 1 − 𝑐𝑜𝑠 𝑥﷮1 + 𝑐𝑜𝑠 𝑥﷯ ﷮﷮ 1 − cos﷮𝑥﷯﷮1 + cos﷮𝑥﷯﷯﷯ We know that Thus, our equation becomes ﷮﷮ 1 − cos﷮𝑥﷯﷮1 + cos﷮𝑥﷯﷯﷯ 𝑑𝑥= ﷮﷮ 2 sin﷮2﷯﷮ 𝑥﷮2﷯﷯﷮2 cos﷮2﷯﷮ 𝑥﷮2﷯﷯﷯﷯ = ﷮﷮ sin﷮2﷯﷮ 𝑥﷮2﷯﷯﷮ cos﷮2﷯﷮ 𝑥﷮2﷯﷯﷯﷯ 𝑑𝑥 = ﷮﷮ tan﷮2﷯﷮ 𝑥﷮2﷯﷯﷯ 𝑑𝑥 = ﷮﷮ sec﷮2﷯﷮ 𝑥﷮2﷯ −1﷯﷯﷯𝑑𝑥 = ﷮﷮ sec﷮2﷯﷮ 𝑥﷮2﷯﷯﷯𝑑𝑥− ﷮﷮𝑑𝑥﷯ = tan﷮2﷯ ﷮ 𝑥﷮2﷯﷯﷮ 1﷮2﷯﷯ −𝑥+𝐶 =𝟐 𝐭𝐚𝐧﷮ 𝒙﷮𝟐﷯﷯ −𝒙+𝑪

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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.