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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 〗/𝑐𝑜𝑠⁡〖5x − 𝑐𝑜𝑠⁡x 〗 = tan x Taking L.H.S. sin⁡〖5x + 〖sin x − 〗⁡2sin⁡3x 〗/𝑐𝑜𝑠⁡〖5x − 𝑐𝑜𝑠⁡x 〗 = 〖(sin〗⁡〖5x + 〖sin x )− 〗⁡2sin⁡3x 〗/𝑐𝑜𝑠⁡〖5x − 𝑐𝑜𝑠⁡x 〗 Solving numerator and denominator separately Taking R.H.S sin⁡〖5x + 〖sin x − 〗⁡2sin⁡3x 〗/𝑐𝑜𝑠⁡〖5x −𝑐𝑜𝑠⁡x 〗 Putting values = (2 sin⁡3𝑥 cos⁡2𝑥 −2 sin⁡3𝑥)/(−2 sin⁡〖3𝑥 sin⁡2𝑥 〗 ) = (2 sin⁡3𝑥 (cos⁡〖2𝑥 − 1)〗)/(−2 sin⁡〖3𝑥 sin⁡2𝑥 〗 ) = ( (cos⁡〖2𝑥 −1)〗)/(−sin⁡2𝑥 ) = ( −(cos⁡〖2𝑥 −1) 〗)/sin⁡2𝑥 = (〖1 − cos〗⁡2𝑥 )/sin⁡2𝑥 = (1 − (1 − 2 sin2⁡𝑥 ) )/(2 cos⁡〖𝑥 〗 sin⁡𝑥 ) = (0 + 2 sin2⁡𝑥)/(2 cos⁡〖𝑥 〗 sin⁡𝑥 ) = (2 sin2⁡𝑥)/(2 cos⁡〖𝑥 〗 sin⁡𝑥 ) = sin⁡〖𝑥 〗/cos⁡〖𝑥 〗 = tan x = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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