Ex 3.3, 16 - Prove that cos 9x - cos 5x / sin 17x - sin 3x - Ex 3.3

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex 3.3, 16 Prove that π‘π‘œπ‘ β‘γ€–9π‘₯ βˆ’γ€– π‘π‘œπ‘ γ€—β‘5π‘₯ γ€—/(𝑠𝑖𝑛 17π‘₯ βˆ’ 𝑠𝑖𝑛⁑3π‘₯ ) =βˆ’π‘ π‘–π‘›β‘γ€–2π‘₯ γ€—/π‘π‘œπ‘ β‘10π‘₯ Taking L.H.S π‘π‘œπ‘ β‘γ€–9π‘₯ βˆ’γ€– π‘π‘œπ‘ γ€—β‘5π‘₯ γ€—/(𝑠𝑖𝑛 17π‘₯ βˆ’ 𝑠𝑖𝑛⁑3π‘₯ ) We solve cos 9x – cos 5x & sin 17x – sin 3x seperately Now, π‘π‘œπ‘ β‘γ€–9π‘₯ βˆ’γ€– π‘π‘œπ‘ γ€—β‘5π‘₯ γ€—/(𝑠𝑖𝑛 17π‘₯ βˆ’ 𝑠𝑖𝑛⁑3π‘₯ ) = (βˆ’2 γ€–sin 〗⁑〖(7x)γ€–sin 〗⁑〖(2x)γ€— γ€—)/(2 π‘π‘œπ‘ β‘γ€–(10x)sin⁑〖 (7x)γ€— γ€— ) = γ€–βˆ’sin〗⁑〖(2x)γ€—/π‘π‘œπ‘ β‘γ€–(10x)γ€— = R.H.S So, L.H.S. = R.H.S. Hence proved

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