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Find ∫e x   √(1 + sin ⁡2x )/(1 + cos ⁡2x ) dx

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/


Integrate e^x root (1 + sin 2x) / (1 + cos 2x) dx - Teachoo

Question 9 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2
Question 9 - CBSE Class 12 Sample Paper for 2018 Boards - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 9 Find 1 ^ (1 + sin 2 )/(1 + cos 2 ) dx 1 ^ (1 + 2 )/(1 + 2 ) dx Putting sin 2x = 2 sin x cos x cos 2x = 2 cos2 x 1 = 1 ^ (1 + 2 sin cos )/(1 + (2 cos^2 1)) dx = 1 ^ (1 + 2 sin cos )/(2 cos^2 ) dx Putting 1 = sin2 x + cos2 x = 1 ^ (sin^2 + cos^2 + 2 sin cos )/(2 cos^2 ) dx = 1 (( + )^2 )/(2 2 )dx = 1/2 1 ^ (sin /( 2 )+cos /( 2 )) = 1/2 1 ("sec sec tan x " ) = 1/2 ^ sec x + c [ ^ ( ( )+ ^ ( )) = ^ ( )+ ] Using (a + b)2 = a2 + b2 + 2ab where a = sin x , b = cos x = 1 ^ (( + )^2 )/(2 2 ) dx = 1/2 1 ^ (( + ))/ 2 dx = 1/2 1 ^ (sin /( 2 )+cos /( 2 )) = 1/2 1 ^ (sin /( ) 1/cos +1/cos ) = 1/2 1 ^ (tan sec +sec ) = 1/2 1 ^ (sec +tan sec ) Using 1 ^ ( ( )+ ^ ( )) = ^ ( )+ Where f(x) = sec x = / ^ sec x + c

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.