Ex 3.3, 19 - Prove sin x + sin 3x / cos x  + cos 3x = tan 2x - cos x + cos y formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex3.3, 19 Prove that γ€–sin x +〗⁑sin⁑3x /(π‘π‘œπ‘ β‘x + π‘π‘œπ‘ β‘3x ) = tan 2x Taking L.H.S. γ€–sin x +〗⁑sin⁑3x /(π‘π‘œπ‘ β‘x + π‘π‘œπ‘ β‘3x ) We solve sin x + sin 3x & cos x + cos 3x seperately Now 𝑠𝑖𝑛⁑〖π‘₯ + 𝑠𝑖𝑛⁑3π‘₯ γ€—/π‘π‘œπ‘ β‘γ€–π‘₯ + π‘π‘œπ‘ β‘3π‘₯ γ€— = (2 γ€– 𝑠𝑖𝑛 〗⁑〖2x π‘π‘œπ‘ β‘γ€–(βˆ’π‘₯)γ€— γ€—)/(2 π‘π‘œπ‘ β‘γ€– 2π‘₯ π‘π‘œπ‘ β‘γ€–(βˆ’π‘₯)γ€— γ€— ) = 𝑠𝑖𝑛⁑〖 2xγ€—/cos⁑〖 2xγ€— = tan 2x = R.H.S Hence L.H.S = R.H.S Hence proved

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