Ex 3.3
Ex 3.3, 2 Important
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Ex 3.3, 5 (i) Important
Ex 3.3, 5 (ii)
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Ex 3.3, 16 Important You are here
Ex 3.3, 17
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Ex 3.3, 21 Important
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Last updated at April 16, 2024 by Teachoo
Ex 3.3, 16 Prove that ๐๐๐ โกใ9๐ฅ โใ ๐๐๐ ใโก5๐ฅ ใ/(๐ ๐๐ 17๐ฅ โ ๐ ๐๐โก3๐ฅ ) =โ๐ ๐๐โกใ2๐ฅ ใ/๐๐๐ โก10๐ฅ Solving L.H.S ๐๐๐ โกใ9๐ฅ โใ ๐๐๐ ใโก5๐ฅ ใ/(๐ ๐๐ 17๐ฅ โ ๐ ๐๐โก3๐ฅ ) We solve cos 9x โ cos 5x & sin 17x โ sin 3x seperately cos 9x โ cos 5x = โ 2 sin ((9x+5x)/2) sin((9xโ5x)/2) = โ 2 sin (14๐ฅ/2) sin (4๐ฅ/2) = โ 2 sin 7x sin (2x) sin 17x โ sin 3x = 2 cos ((17x+3x)/2) sin((17xโ3x)/2) = 2 cos (20๐ฅ/2) sin (14๐ฅ/2) = 2 cos 10x sin 7x Now, ๐๐๐ โกใ9๐ฅ โใ ๐๐๐ ใโก5๐ฅ ใ/(๐ ๐๐ 17๐ฅ โ ๐ ๐๐โก3๐ฅ ) = (โ๐ ใ๐ฌ๐ข๐ง ใโกใ(๐๐ฑ)ใ๐ฌ๐ข๐ง ใโกใ(๐๐ฑ)ใ ใ)/(๐ ๐๐๐โกใ(๐๐๐ฑ)๐ฌ๐ข๐งโกใ (๐๐ฑ)ใ ใ ) = ใโsinใโกใ(2x)ใ/๐๐๐ โกใ(10x)ใ = R.H.S So, L.H.S. = R.H.S. Hence proved