Ex 7.2, 39 - Integration dx / sin2 x cos2 x equals - Integration by substitution - Trignometric - Normal

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 39 ﷮﷮ 𝑑𝑥﷮𝑠𝑖𝑛2 𝑥 𝑐𝑜𝑠2 𝑥﷯﷯ equals • tan x + cot x + C (B) tan x – cot x + C (C) tan x cot x + C (D) tan x – cot 2x + C Step 1: Simplify the given function ﷮﷮ 𝑑𝑥﷮ sin﷮2﷯ 𝑥 cos﷮2﷯﷮𝑥﷯﷯﷯ = ﷮﷮ 1﷮ sin﷮2﷯ 𝑥 cos﷮2﷯﷮𝑥﷯﷯ . 𝑑𝑥﷯ = ﷮﷮ sin﷮2﷯ 𝑥 + cos﷮2﷯﷮𝑥﷯﷮ sin﷮2﷯ 𝑥 cos﷮2﷯﷮𝑥﷯﷯ . 𝑑𝑥﷯ = ﷮﷮ sin﷮2﷯ 𝑥﷮ sin﷮2﷯ 𝑥 cos﷮2﷯﷮𝑥﷯﷯ . 𝑑𝑥﷯ + ﷮﷮ cos﷮2﷯﷮𝑥﷯﷮ sin﷮2﷯ 𝑥 cos﷮2﷯﷮𝑥﷯﷯ . 𝑑𝑥﷯ = ﷮﷮ 1﷮ cos﷮2﷯﷮𝑥﷯﷯ . 𝑑𝑥﷯ + ﷮﷮ 1﷮ sin﷮2﷯ 𝑥﷯ . 𝑑𝑥﷯ = ﷮﷮ sec﷮2﷯﷮𝑥﷯. 𝑑𝑥﷯ + ﷮﷮𝑐𝑜𝑠𝑒 𝑐﷮2﷯𝑥 . 𝑑𝑥﷯ = tan﷮𝑥﷯+𝐶1− cot﷮𝑥﷯+𝐶2 = tan﷮𝑥﷯− cot﷮𝑥﷯+𝐶 ∴ Option B is correct.

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