Ex 7.3, 16 - Integrate tan4 x dx - Chapter 7 Class 12 - Integration using trigo identities - sin^2,cos^2 etc formulae

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.3, 16 ﷮﷮ tan﷮4﷯ 𝑥﷯𝑑𝑥 ﷮﷮ tan﷮4﷯ 𝑥﷯𝑑𝑥= ﷮﷮ tan﷮2﷯ 𝑥 . tan﷮2﷯𝑥﷯𝑑𝑥 = ﷮﷮ sec﷮2﷯𝑥﷮−1﷯﷯ tan﷮2﷯﷮𝑥﷯﷯𝑑𝑥 = ﷮﷮ sec﷮2﷯﷮𝑥﷯. tan﷮2﷯﷮𝑥﷯− tan﷮2﷯﷮𝑥﷯﷯﷯𝑑𝑥 = ﷮﷮ tan﷮2﷯﷮𝑥﷯. sec﷮2﷯﷮𝑥﷯﷯𝑑𝑥− ﷮﷮ tan﷮2﷯𝑥﷯𝑑𝑥 Now, ﷮﷮ tan﷮4﷯ 𝑥﷯𝑑𝑥= ﷮﷮ tan﷮2﷯ 𝑥 . sec﷮2﷯𝑥﷯𝑑𝑥− ﷮﷮ tan﷮2﷯ 𝑥﷯ 𝑑𝑥 = tan﷮3﷯﷮𝑥﷯﷮3﷯+𝐶1− tan﷮𝑥﷯−𝑥+𝐶2﷯ = tan﷮3﷯﷮𝑥﷯﷮3﷯ − tan﷮𝑥﷯+𝑥+𝐶1−𝐶2 = 𝒕𝒂𝒏﷮𝟑﷯﷮𝒙﷯﷮𝟑﷯ − 𝒕𝒂𝒏﷮𝒙﷯+𝒙+𝑪

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