# Example 41 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 41 Evaluate cot + tan cot + tan = cot + 1 cot = cot + 1 cot = tan cot +1 Let tan = 2 Differentiating both sides . . . . sec 2 =2 1+ tan 2 =2 . 1+ 2 2 =2 . 1+ 4 =2 . 1+ 4 =2 = 2 1 + 4 . Putting values of t & dt, we get 2 cot +1 = 2 1 tan +1 = 1 2 +1 = 1 2 +1 = 1 + 2 2 = 1 + 2 2 2 1 + 2 . = 2 1 + 2 1 + 4 = 2 1 + 2 1 + 4 Dividing numerator and denominator by 2 = 2 1 + 2 2 1 + 4 2 . = 2 1 2 + 1 1 2 + 2 . = 2 1 2 + 1 1 2 + 2 . = 2 1 + 1 2 2 + 1 2 + 2 2 . = 2 1 + 1 2 2 + 1 2 2 1 + 2 . = 2 1 + 1 2 1 2 + 2 . = 2 1 + 1 2 1 2 + 2 2 . Let 1 = Differentiating both sides . . . . 1+ 1 2 = = 1 + 1 2 Putting the values of 1 t t and dt, we get = 2 1 + 1 2 2 + 2 2 . = 2 1 + 1 2 2 + 2 2 1 1 2 = 2 1 2 + 2 2 . = 2 1 2 tan 1 2 + 1 = 2 2 tan 1 2 +2 1 = 2 tan 1 1 2 +2 1 = 2 tan 1 2 1 2 + = 2 tan 1 tan 1 2 tan + = +

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.