Misc 39 (MCQ) - Chapter 7 Class 12 Integrals

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Misc 39 (MCQ) - Intgeral cos 2x / (sin x + cos x) dx is equal - Miscellaneous

part 2 - Misc 39 (MCQ) - Miscellaneous - Serial order wise - Chapter 7 Class 12 Integrals

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Misc 39 Choose the correct answer ∫▒cos⁡2𝑥/((sin⁡𝑥 + cos⁡𝑥 )^2 ) 𝑑𝑥 is equal to (A) (−1)/(sin⁡𝑥 + cos⁡𝑥 )+𝐶 (B) log⁡|sin⁡𝑥+cos⁡𝑥 |+𝐶 (C) log⁡|sin⁡𝑥−cos⁡𝑥 |+𝐶 (D) " " 1/(sin⁡𝑥 + cos⁡𝑥 )^2 ∫1▒cos⁡2𝑥/(cos⁡𝑥 + sin⁡𝑥 )^2 =∫1▒(cos^2⁡𝑥 − sin^2⁡𝑥)/(cos⁡𝑥 + sin⁡𝑥 )^2 𝑑𝑥 =∫1▒(cos⁡𝑥 − sin⁡𝑥 )(cos⁡𝑥 + sin⁡𝑥 )/(cos⁡𝑥 + sin⁡𝑥 )^2 𝑑𝑥 =∫1▒(cos⁡𝑥 − sin⁡𝑥)/(cos⁡𝑥 + sin⁡𝑥 ) 𝑑𝑥 Let cos⁡𝑥+sin⁡𝑥=𝑡 Diff w.r.t. x −sin⁡𝑥+cos⁡𝑥=𝑑𝑡/𝑑𝑥 𝑑𝑥=1/((cos⁡𝑥 − sin⁡𝑥 ) ) 𝑑𝑡 Hence, our equation becomes =∫1▒((cos⁡𝑥 − sin⁡𝑥 ))/𝑑𝑡 ×𝑑𝑡/(cos⁡𝑥 − sin⁡𝑥 ) =∫1▒1/𝑡 𝑑𝑡 =log⁡𝑡+𝐶 Putting value of 𝑡=𝑐𝑜𝑠⁡𝑥+𝑠𝑖𝑛⁡𝑥 =log⁡|cos⁡𝑥+sin⁡𝑥 |+𝐶 Hence correct answer is B.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo