Example 17 - Prove sin 5x - 2 sin 3x + sin x / cos 5x - cos x - cos x + cos y formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Example 17 Prove that sin 5x 2sin 3x + sin x / 5x x = tan x Taking L.H.S. sin 5x + sin x 2sin 3x / 5x x = (sin 5x + sin x ) 2sin 3x / 5x x Solving numerator and denominator separately Taking R.H.S sin 5x + sin x 2sin 3x / 5x x Putting values = (2 sin 3 cos 2 2 sin 3 )/( 2 sin 3 sin 2 ) = (2 sin 3 (cos 2 1) )/( 2 sin 3 sin 2 ) = ( (cos 2 1) )/( sin 2 ) = ( (cos 2 1) )/sin 2 = ( 1 cos 2 )/sin 2 = (1 (1 2 sin2 ) )/(2 cos sin ) = (0 + 2 sin2 )/(2 cos sin ) = (2 sin2 )/(2 cos sin ) = sin /cos = tan x = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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