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Example 16 - Chapter 3 Class 11 Trigonometric Functions
Last updated at Feb. 13, 2020 by Teachoo
Transcript
Example 16 Prove that ๐๐๐ โกใ7๐ฅ + ๐๐๐ โก5๐ฅ ใ/๐ ๐๐โกใ7๐ฅ โ ๐ ๐๐โก5๐ฅ 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 (๐ฅ + ๐ฆ)/2 cos (๐ฅ โ ๐ฆ)/2 Putting x = 7x & y = 5x cos 7x + cos 5x = 2 cos ((7๐ฅ + 5๐ฅ)/2) cos ((7๐ฅ โ 5๐ฅ)/2) = 2 cos (12๐ฅ/2) cos (2๐ฅ/2) = 2 cos 6x cos x sin x โ sin y = 2 cos (๐ฅ + ๐ฆ)/2 sin (๐ฅ โ ๐ฆ)/2 Putting x = 7x & y = 5x sin 7x โ sin 5x = 2 cos ((7๐ฅ + 5๐ฅ)/2) sin((7๐ฅ โ 5๐ฅ)/2) = 2 cos (12๐ฅ/2) sin (2๐ฅ/2) = 2 cos 6x sin x Now ใ๐๐๐ ใโกใ7๐ฅ + ๐๐๐ โก5๐ฅ ใ/๐ ๐๐โกใ7๐ฅ โ ๐ ๐๐โก5๐ฅ ใ = (2 ใ ๐๐๐ ใโกใ6x ๐๐๐ โก๐ฅ ใ)/(2 ๐๐๐ โกใ 6๐ฅ si๐โก๐ฅ ใ ) = ๐๐๐ โกใ ๐ฅใ/๐ ๐๐โกใ ๐ฅใ = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved
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Chapter 3 Class 11 Trigonometric Functions
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About the Author
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.