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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 3.3, 17 Prove that ๐‘ ๐‘–๐‘›โกใ€–5๐‘ฅ + ๐‘ ๐‘–๐‘›โก3๐‘ฅ ใ€—/๐‘๐‘œ๐‘ โกใ€–5๐‘ฅ + ๐‘๐‘œ๐‘ โก3๐‘ฅ ใ€— = tan 4x Solving L.H.S. ๐‘ ๐‘–๐‘›โกใ€–5๐‘ฅ + ๐‘ ๐‘–๐‘›โก3๐‘ฅ ใ€—/๐‘๐‘œ๐‘ โกใ€–5๐‘ฅ + ๐‘๐‘œ๐‘ โก3๐‘ฅ ใ€— We solve sin 5x + sin 3x & cos 5x + cos 3x seperately sin 5x + sin 3x = 2 sin ((5x+3x)/2) cos ((5xโˆ’3x)/2) = 2 sin (8๐‘ฅ/2) cos (2๐‘ฅ/2) = 2 sin 4x cos x cos 5x + cos 3x = 2 cos ((5x+3x)/2) cos ((5xโˆ’3x)/2) = 2 cos (8๐‘ฅ/2) cos (2๐‘ฅ/2) = 2 cos 4x cos (x) Now ๐’”๐’Š๐’โกใ€–๐Ÿ“๐’™ + ๐’”๐’Š๐’โก๐Ÿ‘๐’™ ใ€—/๐’„๐’๐’”โกใ€–๐Ÿ“๐’™ + ๐’„๐’๐’”โก๐Ÿ‘๐’™ ใ€— = (2 ใ€– ๐‘ ๐‘–๐‘› ใ€—โกใ€–4x ๐‘๐‘œ๐‘ โก๐‘ฅ ใ€—)/(2 ๐‘๐‘œ๐‘ โกใ€– 4๐‘ฅ ๐‘๐‘œ๐‘ โก๐‘ฅ ใ€— ) = ๐’”๐’Š๐’โกใ€– ๐Ÿ’๐’™ใ€—/๐œ๐จ๐ฌโกใ€– ๐Ÿ’๐’™ใ€— = tan 4x = R.H.S Hence L.H.S = R.H.S Hence proved

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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.