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Ex 7.2, 25 - Integrate 1 / cos2 x (1 - tan x)2  - Ex 7.2

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 25 1﷮𝑐𝑜𝑠2𝑥 1 − tan﷮𝑥﷯﷯﷮2﷯﷯ Step 1: Let 1 − tan﷮𝑥﷯=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 0− sec﷮2﷯﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ − sec﷮2﷯﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮ −sec﷮2﷯﷮𝑥﷯﷯ 𝑑𝑥= − 𝑑𝑡﷮ 1﷮ cos﷮2﷯﷮𝑥﷯﷯﷯﷯ 𝑑𝑥=− cos﷮2﷯﷮𝑥﷯ 𝑑𝑡 Step 2: Integrating the function ﷮﷮ 1﷮𝑐𝑜𝑠2𝑥 1 − tan﷮𝑥﷯﷯﷮2﷯﷯﷯. 𝑑𝑥 Putting 1− 𝑡𝑎𝑛﷮𝑥﷯=𝑡 & 𝑑𝑥=− cos﷮2﷯﷮𝑥﷯ 𝑑𝑡 = ﷮﷮ 1﷮𝑐𝑜𝑠2𝑥 𝑡﷯﷮2﷯﷯﷯. − cos﷮2﷯﷮𝑥﷯ 𝑑𝑡 = ﷮﷮− 1﷮ 𝑡﷮2﷯﷯﷯ . 𝑑𝑡 = − ﷮﷮ 𝑡﷮−2﷯﷯ . 𝑑𝑡 = − 𝑡﷮−2 + 1﷯﷮−2 + 1﷯ +𝐶 = − 𝑡﷮−1﷯﷮−1﷯ +𝐶 = 𝑡﷮−1﷯ +𝐶 = 1﷮𝑡﷯ +𝐶 = 𝟏﷮ 𝟏 − 𝐭𝐚𝐧﷮𝒙﷯﷯﷯ +𝑪

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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