Example 3 - Chapter 7 Class 12 Integrals - Part 3

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Example 3 Find the following integrals: (iii) ∫▒(1 − sin⁡𝑥)/cos^2⁡𝑥 𝑑𝑥 ∫▒(1 − sin⁡𝑥)/cos^2⁡𝑥 𝑑𝑥 = ∫▒(1/cos^2⁡𝑥 − sin⁡𝑥/cos^2⁡𝑥 ) 𝑑𝑥 = ∫▒(sec^2⁡𝑥−sin⁡𝑥/𝑐𝑜𝑠⁡𝑥 . 1/𝑐𝑜𝑠⁡𝑥 ) 𝑑𝑥 = ∫▒(sec^2⁡𝑥−tan⁡𝑥 sec⁡𝑥 ) 𝑑𝑥 = 𝒕𝒂𝒏⁡𝒙−𝒔𝒆𝒄⁡𝒙+𝑪 As ∫1▒〖𝑠𝑒𝑐^2 𝑥 𝑑𝑥〗=tan⁡𝑥+𝐶 ∫1▒〖𝑠𝑒𝑐 𝑥 tan⁡〖𝑥 𝑑𝑥〗 〗=𝑠𝑒𝑐 𝑥+𝐶

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