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Ex 3.3, 8 - Chapter 3 Class 11 Trigonometry - Ex 3.3

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex 3.3, 8 Prove that cos⁑〖 (Ο€ + π‘₯) cos⁑〖(βˆ’ π‘₯)γ€— γ€—/(sin⁑〖 (Ο€ βˆ’ π‘₯)γ€— cos⁑〖"( " Ο€/2 " + " π‘₯")" γ€— ) = cot2 π‘₯ Taking L.H.S. π‘π‘œπ‘ β‘γ€–(πœ‹ + π‘₯) γ€–π‘π‘œπ‘  〗⁑〖(βˆ’π‘₯)γ€— γ€—/(𝑠𝑖𝑛⁑(πœ‹ βˆ’ π‘₯) π‘π‘œπ‘ β‘γ€–"(" πœ‹/2 " +" π‘₯")" γ€— ) Putting Ο€ = 180Β° = π‘π‘œπ‘ β‘γ€–(180 + π‘₯) γ€–π‘π‘œπ‘  〗⁑〖(βˆ’π‘₯)γ€— γ€—/(𝑠𝑖𝑛⁑(180 βˆ’ π‘₯) π‘π‘œπ‘ β‘γ€–"(" 90" + " π‘₯")" γ€— ) = (βˆ’π‘π‘œπ‘ β‘γ€–π‘₯ Γ— π‘π‘œπ‘ β‘π‘₯ γ€—)/((sin⁑〖π‘₯) Γ—γ€–( βˆ’sin〗⁑π‘₯) γ€— ) = (βˆ’ π‘π‘œπ‘ 2π‘₯)/(βˆ’ 𝑠𝑖𝑛2π‘₯) = cot2x = R.H.S. Hence proved

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