# Integrate cos 2x

Integral of Cos(2x)
Integral of Cos(2x)

Ex 7.3, 13 – Chapter 7 Class 12 Integrals

Last updated at May 29, 2023 by Teachoo

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Ex 7.3, 13 Important You are here

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Ex 7.3, 23 (MCQ)

Ex 7.3, 24 (MCQ) Important

Last updated at May 29, 2023 by Teachoo

Ex 7.3, 13 Integrate the function cos〖2𝑥 − cos2𝛼 〗/cos〖𝑥 − cos𝛼 〗 ∫1▒〖cos〖2𝑥 − cos2𝛼 〗/cos〖𝑥 − cos𝛼 〗 ” ” 𝑑𝑥〗 =∫1▒((2 cos^2〖𝑥 − 1〗 ) − (2 cos^2〖𝛼 − 1〗 ))/(cos𝑥 − cos𝛼 ) 𝑑𝑥 =∫1▒(2 cos^2〖𝑥 − 1〗 − 2 cos^2〖𝛼 + 1〗)/(cos𝑥 − cos𝛼 ) 𝑑𝑥 =∫1▒(2 cos^2𝑥 − 2 cos^2𝛼 + 1 − 1)/(cos𝑥 − cos𝛼 ) 𝑑𝑥 =∫1▒2(cos^2𝑥 − cos^2𝛼 )/(cos𝑥 − cos𝛼 ) 𝑑𝑥 =2∫1▒(cos^2𝑥 − cos^2𝛼)/(cos𝑥 − cos𝛼 ) 𝑑𝑥 =2∫1▒((𝑐𝑜𝑠𝑥 − 𝑐𝑜𝑠𝛼 ) (𝑐𝑜𝑠𝑥 + 𝑐𝑜𝑠𝛼 ))/((𝑐𝑜𝑠𝑥 − 𝑐𝑜𝑠𝛼 ) ) 𝑑𝑥 =2∫1▒(𝑐𝑜𝑠𝑥+𝑐𝑜𝑠𝛼 ) 𝑑𝑥 =2(∫1▒𝑐𝑜𝑠𝑥 𝑑𝑥+∫1▒𝑐𝑜𝑠𝛼 𝑑𝑥) =2(∫1▒𝑐𝑜𝑠𝑥 𝑑𝑥+𝑐𝑜𝑠𝛼 ∫1▒1. 𝑑𝑥) =𝟐(𝒔𝒊𝒏𝒙+𝒙𝒄𝒐𝒔 𝜶)” +” 𝑪 (𝑐𝑜𝑠2𝜃=2 〖𝑐𝑜𝑠〗^2𝜃−1)

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