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Ex 3.3, 17 - Prove sin 5x + sin 3x / cos 5x + cos 3x = tan 4x - cos x + cos y formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex3.3, 17 Prove that 𝑠𝑖𝑛⁑〖5π‘₯ + 𝑠𝑖𝑛⁑3π‘₯ γ€—/π‘π‘œπ‘ β‘γ€–5π‘₯ + π‘π‘œπ‘ β‘3π‘₯ γ€— = tan 4x Taking L.H.S. 𝑠𝑖𝑛⁑〖5π‘₯ + 𝑠𝑖𝑛⁑3π‘₯ γ€—/π‘π‘œπ‘ β‘γ€–5π‘₯ + π‘π‘œπ‘ β‘3π‘₯ γ€— We solve sin 5x + sin 3x & cos 5x + cos 3x seperately Now 𝑠𝑖𝑛⁑〖5π‘₯ + 𝑠𝑖𝑛⁑3π‘₯ γ€—/π‘π‘œπ‘ β‘γ€–5π‘₯ + π‘π‘œπ‘ β‘3π‘₯ γ€— = (2 γ€– 𝑠𝑖𝑛 〗⁑〖4x π‘π‘œπ‘ β‘π‘₯ γ€—)/(2 π‘π‘œπ‘ β‘γ€– 4π‘₯ π‘π‘œπ‘ β‘π‘₯ γ€— ) = 𝑠𝑖𝑛⁑〖 4xγ€—/cos⁑〖 4xγ€— = tan 4x = R.H.S Hence L.H.S = R.H.S Hence proved

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