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Example 16 - Prove cos 7x + cos 5x / sin 7x - sin 5x = cot x - cos x + cos y formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Example 16 Prove that π‘π‘œπ‘ β‘γ€–7π‘₯ + π‘π‘œπ‘ β‘5π‘₯ γ€—/𝑠𝑖𝑛⁑〖7π‘₯ βˆ’ 𝑠𝑖𝑛⁑5π‘₯ γ€— = cot x Taking L.H.S. γ€–π‘π‘œπ‘  〗⁑〖7π‘₯ + π‘π‘œπ‘ β‘5π‘₯ γ€—/𝑠𝑖𝑛⁑〖7π‘₯ βˆ’ 𝑠𝑖𝑛⁑5π‘₯ γ€— We solve cos 7x + cos 5x & sin 7x – sin 5x seperately Now γ€–π‘π‘œπ‘  〗⁑〖7π‘₯ + π‘π‘œπ‘ β‘5π‘₯ γ€—/𝑠𝑖𝑛⁑〖7π‘₯ βˆ’ 𝑠𝑖𝑛⁑5π‘₯ γ€— = (2 γ€– π‘π‘œπ‘  〗⁑〖6x π‘π‘œπ‘ β‘π‘₯ γ€—)/(2 π‘π‘œπ‘ β‘γ€– 6π‘₯ si𝑛⁑π‘₯ γ€— ) = π‘π‘œπ‘ β‘γ€– xγ€—/sin⁑〖 xγ€— = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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