Ex 7.3, 23 - Integration sin2 x - cos2 x / sin2 x cos2 x dx - Integration using trigo identities - sin^2,cos^2 etc formulae

  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.3, 23 ﷮﷮ 𝑠𝑖𝑛2 𝑥−𝑐𝑜𝑠2 𝑥﷮𝑠𝑖𝑛2 𝑥 𝑐𝑜𝑠2 𝑥﷯﷯ 𝑑𝑥 is equal to (A)tan x + cot x + C (B) tan x + cosec x + C (C) − tan x + cot x + C (D) tan x + sec x + C ﷮﷮ sin﷮2﷯﷮𝑥﷯ − cos﷮2﷯﷮𝑥﷯﷮ sin﷮2﷯﷮𝑥﷯ cos﷮2﷯﷮𝑥﷯﷯﷯𝑑𝑥 = ﷮﷮ sin﷮2﷯﷮𝑥﷯﷮ sin﷮2﷯﷮𝑥﷯ cos﷮2﷯﷮𝑥﷯﷯ − cos﷮2﷯﷮𝑥﷯﷮ sin﷮2﷯﷮𝑥﷯ cos﷮2﷯﷮𝑥﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ 1﷮ cos﷮2﷯﷮𝑥﷯﷯ − 1﷮ sin﷮2﷯﷮𝑥﷯﷯﷯﷯𝑑𝑥 = ﷮﷮ sec﷮2﷯﷮𝑥﷯﷯𝑑𝑥− ﷮﷮𝑐𝑜𝑠𝑒 𝑐﷮2﷯𝑥﷯𝑑𝑥 = tan﷮𝑥﷯− − cot﷮𝑥﷯﷯+𝐶 = tan﷮𝑥﷯+ cot﷮𝑥﷯+𝐶 Hence correct answer is (A).

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