Check sibling questions

Ex 7.3, 20 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at March 23, 2023 by

Ex 7.3, 20 - Integrate cos 2x / (cos x + sin x)^2 - NCERT Maths

Ex 7.3, 20 - Chapter 7 Class 12 Integrals - Part 2

Get live Maths 1-on-1 Classs - Class 6 to 12

Book 30 minute class for ₹ 499 ₹ 299

Transcript

Ex 7.3, 20 Integrate the function cos⁡2𝑥/(cos⁡〖𝑥 〗+ sin⁡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 Differentiating w.r.t. x (𝑐𝑜𝑠⁡2𝜃=〖𝑐𝑜𝑠〗^2⁡𝜃−〖𝑠𝑖𝑛〗^2⁡𝜃) −sin⁡𝑥+cos⁡𝑥=𝑑𝑡/𝑑𝑥 (cos⁡𝑥−sin⁡𝑥 )𝑑𝑥=𝑑𝑡 𝑑𝑥=1/((cos⁡𝑥 − sin⁡𝑥 ) ) 𝑑𝑡 Thus, our equation becomes =∫1▒((cos⁡𝑥 − sin⁡𝑥 ))/𝑡 ×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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.