Example 3 - Find integrals (i) sin x + cos x dx - Class 12 - Using Trignometric Formulaes

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Example 3 Find the following integrals: • ﷮﷮ sin﷮x﷯+ cos﷮x﷯﷯﷯ dx ﷮﷮ sin﷮𝑥﷯+ cos﷮𝑥﷯﷯﷯ 𝑑𝑥 = ﷮﷮ sin﷮𝑥﷯﷯﷯𝑑𝑥+ ﷮﷮ (cos﷮𝑥﷯) ﷯𝑑𝑥 =− 𝐜𝐨𝐬﷮𝒙﷯+ 𝐬𝐢𝐧﷮𝒙﷯+𝑪 Example 3 Find the following integrals: (ii) ﷮﷮𝑐𝑜𝑠𝑒𝑐 𝑥 𝑐𝑜𝑠𝑒𝑐 𝑥+ cot﷮𝑥﷯﷯﷯𝑑𝑥 ﷮﷮𝑐𝑜𝑠𝑒𝑐 𝑥 𝑐𝑜𝑠𝑒𝑐 𝑥+ cot﷮𝑥﷯﷯﷯𝑑𝑥 = ﷮﷮ 𝑐𝑜𝑠𝑒𝑐 𝑥+𝑐𝑜𝑠𝑒𝑐 𝑥 cot﷮𝑥﷯﷯﷯𝑑𝑥 = ﷮﷮𝑐𝑜𝑠𝑒 𝑐﷮2﷯ 𝑥 𝑑𝑥﷯+ ﷮﷮𝑐𝑜𝑠𝑒𝑐 𝑥 cot﷮𝑥﷯﷯𝑑𝑥 = − 𝐜𝐨𝐭﷮𝒙﷯ −𝒄𝒐𝒔𝒆𝒄 𝒙+𝑪 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

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.