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Chapter 7 Class 12 Integrals
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Ex 7.3, 13 - Integrate cos 2x - cos 2a / cos x - cos a - Ex 7.3

Ex 7.3, 13 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.3, 13 Integrate the function cos⁑〖2π‘₯ βˆ’ cos⁑2𝛼 γ€—/cos⁑〖π‘₯ βˆ’ cos⁑𝛼 γ€— ∫1β–’γ€–cos⁑〖2π‘₯ βˆ’ cos⁑2𝛼 γ€—/cos⁑〖π‘₯ βˆ’ cos⁑𝛼 γ€— " " 𝑑π‘₯γ€— =∫1β–’((2 cos^2⁑〖π‘₯ βˆ’ 1γ€— ) βˆ’ (2 cos^2⁑〖𝛼 βˆ’ 1γ€— ))/(cos⁑π‘₯ βˆ’ cos⁑𝛼 ) 𝑑π‘₯ =∫1β–’(2 cos^2⁑〖π‘₯ βˆ’ 1γ€— βˆ’ 2 cos^2⁑〖𝛼 + 1γ€—)/(cos⁑π‘₯ βˆ’ cos⁑𝛼 ) 𝑑π‘₯ =∫1β–’(2 cos^2⁑π‘₯ βˆ’ 2 cos^2⁑𝛼 + 1 βˆ’ 1)/(cos⁑π‘₯ βˆ’ cos⁑𝛼 ) 𝑑π‘₯ =∫1β–’2(cos^2⁑π‘₯ βˆ’ cos^2⁑𝛼 )/(cos⁑π‘₯ βˆ’ cos⁑𝛼 ) 𝑑π‘₯ =2∫1β–’(cos^2⁑π‘₯ βˆ’ cos^2⁑𝛼)/(cos⁑π‘₯ βˆ’ cos⁑𝛼 ) 𝑑π‘₯ =2∫1β–’((π‘π‘œπ‘ β‘π‘₯ βˆ’ π‘π‘œπ‘ β‘π›Ό ) (π‘π‘œπ‘ β‘π‘₯ + π‘π‘œπ‘ β‘π›Ό ))/((π‘π‘œπ‘ β‘π‘₯ βˆ’ π‘π‘œπ‘ β‘π›Ό ) ) 𝑑π‘₯ =2∫1β–’(π‘π‘œπ‘ β‘π‘₯+π‘π‘œπ‘ β‘π›Ό ) 𝑑π‘₯ =2(∫1β–’π‘π‘œπ‘ β‘π‘₯ 𝑑π‘₯+∫1β–’π‘π‘œπ‘ β‘π›Ό 𝑑π‘₯) =2(∫1β–’π‘π‘œπ‘ β‘π‘₯ 𝑑π‘₯+π‘π‘œπ‘ β‘π›Ό ∫1β–’1. 𝑑π‘₯) =𝟐(π’”π’Šπ’β‘π’™+𝒙⁑𝒄𝒐𝒔 𝜢)" +" π‘ͺ (π‘π‘œπ‘ β‘2πœƒ=2 γ€–π‘π‘œπ‘ γ€—^2β‘πœƒβˆ’1)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.