Ex 3.3, 17 - Chapter 3 Class 11 Trigonometric Functions
Last updated at Dec. 13, 2024 by Teachoo
Last updated at Dec. 13, 2024 by Teachoo
Ex 3.3, 17 Prove that ๐ ๐๐โกใ5๐ฅ + ๐ ๐๐โก3๐ฅ ใ/๐๐๐ โกใ5๐ฅ + ๐๐๐ โก3๐ฅ ใ = tan 4x Solving L.H.S. ๐ ๐๐โกใ5๐ฅ + ๐ ๐๐โก3๐ฅ ใ/๐๐๐ โกใ5๐ฅ + ๐๐๐ โก3๐ฅ ใ We solve sin 5x + sin 3x & cos 5x + cos 3x seperately sin 5x + sin 3x = 2 sin ((5x+3x)/2) cos ((5xโ3x)/2) = 2 sin (8๐ฅ/2) cos (2๐ฅ/2) = 2 sin 4x cos x cos 5x + cos 3x = 2 cos ((5x+3x)/2) cos ((5xโ3x)/2) = 2 cos (8๐ฅ/2) cos (2๐ฅ/2) = 2 cos 4x cos (x) Now ๐๐๐โกใ๐๐ + ๐๐๐โก๐๐ ใ/๐๐๐โกใ๐๐ + ๐๐๐โก๐๐ ใ = (2 ใ ๐ ๐๐ ใโกใ4x ๐๐๐ โก๐ฅ ใ)/(2 ๐๐๐ โกใ 4๐ฅ ๐๐๐ โก๐ฅ ใ ) = ๐๐๐โกใ ๐๐ใ/๐๐จ๐ฌโกใ ๐๐ใ = tan 4x = R.H.S Hence L.H.S = R.H.S Hence proved
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