# Ex 7.2, 34

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 7.2, 34 tan𝑥 sin𝑥 cos𝑥 tan𝑥 sin𝑥 cos𝑥 The given function cannot be integrated by direct substitution, Step 1: Simplify the given function tan𝑥 sin𝑥 cos𝑥 = tan𝑥 sin𝑥 cos𝑥. cos𝑥 cos𝑥 = tan𝑥 sin𝑥 . cos2𝑥 cos𝑥 = tan𝑥 cos2𝑥 . sin 𝑥 cos𝑥 = tan𝑥 cos2𝑥 . tan𝑥 = tan𝑥 12 − 1 × 1 cos2𝑥 = tan𝑥 −12 × 1 cos2𝑥 = tan𝑥 −12 × sec2𝑥 ∴ tan𝑥 sin𝑥 cos𝑥 = tan𝑥 −12 × sec2𝑥 Step 2: Integrating the function tan𝑥 sin𝑥 cos𝑥 . 𝑑𝑥 = tan𝑥 −12 × sec2𝑥. 𝑑𝑥 Let tan𝑥 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 sec2𝑥= 𝑑𝑡𝑑𝑥 𝑑𝑥= 𝑑𝑡 sec2𝑥 Thus, our equation becomes ∴ tan𝑥 −12 . sec2𝑥. 𝑑𝑥 = 𝑡 −12 . sec2𝑥. 𝑑𝑡 sec2𝑥 = 𝑡 −12 . 𝑑𝑡 = 𝑡− 12 +1− 12 +1 + 𝐶 = 𝑡 12 12 + 𝐶 = 2𝑡 12+ 𝐶 = 2 𝑡+ 𝐶 = 𝟐 𝐭𝐚𝐧𝒙+ 𝑪

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.