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  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise

Transcript

Example 16 Prove that ๐‘๐‘œ๐‘ โกใ€–7๐‘ฅ + ๐‘๐‘œ๐‘ โก5๐‘ฅ ใ€—/๐‘ ๐‘–๐‘›โกใ€–7๐‘ฅ โˆ’ ๐‘ ๐‘–๐‘›โก5๐‘ฅ ใ€— = cot x Taking L.H.S. We solve cos 7x + cos 5x & sin 7x โ€“ sin 5x separately cos x + cos y = 2 cos (๐‘ฅ + ๐‘ฆ)/2 cos (๐‘ฅ โˆ’ ๐‘ฆ)/2 Putting x = 7x & y = 5x cos 7x + cos 5x = 2 cos ((7๐‘ฅ + 5๐‘ฅ)/2) cos ((7๐‘ฅ โˆ’ 5๐‘ฅ)/2) = 2 cos (12๐‘ฅ/2) cos (2๐‘ฅ/2) = 2 cos 6x cos x sin x โ€“ sin y = 2 cos (๐‘ฅ + ๐‘ฆ)/2 sin (๐‘ฅ โˆ’ ๐‘ฆ)/2 Putting x = 7x & y = 5x sin 7x โ€“ sin 5x = 2 cos ((7๐‘ฅ + 5๐‘ฅ)/2) sin((7๐‘ฅ โˆ’ 5๐‘ฅ)/2) = 2 cos (12๐‘ฅ/2) sin (2๐‘ฅ/2) = 2 cos 6x sin x Now ใ€–๐‘๐‘œ๐‘  ใ€—โกใ€–7๐‘ฅ + ๐‘๐‘œ๐‘ โก5๐‘ฅ ใ€—/๐‘ ๐‘–๐‘›โกใ€–7๐‘ฅ โˆ’ ๐‘ ๐‘–๐‘›โก5๐‘ฅ ใ€— = (2 ใ€– ๐‘๐‘œ๐‘  ใ€—โกใ€–6x ๐‘๐‘œ๐‘ โก๐‘ฅ ใ€—)/(2 ๐‘๐‘œ๐‘ โกใ€– 6๐‘ฅ si๐‘›โก๐‘ฅ ใ€— ) = ๐‘๐‘œ๐‘ โกใ€– ๐‘ฅใ€—/๐‘ ๐‘–๐‘›โกใ€– ๐‘ฅใ€— = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.