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Misc 5 - Prove sin x + sin 3x + sin5x + sin 7x = 4 cos x - cos x + cos y formula

Misc 5 - Chapter 3 Class 11 Trigonometric Functions - Part 2

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Misc 5 Prove that: sin x + sin 3x + sin5x + sin 7x = 4 cos x sin 2x sin 4x Solving L.H.S sin x + sin 3x + sin5x + sin 7x = (sin 7x + sin x ) + (sin 5x + sin 3x) = (2 sin ((7x + x)/2) cos((7x x)/2) ) + (2 sin ((5x + 3x)/2) cos ((5x 3x)/2) ) = 2 sin 8 /2 cos 6 /2 + 2 sin 8 /2 cos 2 /2 = 2 sin 4x cos 3x + 2 sin 4x cos x = 2 sin 4x [ cos 3x + cos x] = 2sin 4x [ 2cos ((3x + x)/2) cos ((3x x)/2) ] = 2sin 4x [ 2cos (4x/2) cos (4x/2) ] = 2 sin 4x [2cos 2x . cos x ] = 2 sin 4x . 2 cos 2x . cos x = 4 cos x . cos 2x . sin 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.