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Ex 3.3, 7 - Prove tan (pi/4 + x) / tan (pi/4 - x) = (1 + tan x)2 - (x + y) formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex 3.3, 7 Prove that: (tan"(" πœ‹/4 " + " π‘₯")" )/(tan"(" Ο€/4 " βˆ’ " π‘₯")" ) = ((1+ tan" " π‘₯)/(1βˆ’ tan" " π‘₯))^2 Solving L.H.S. (tan⁑ (πœ‹/4 + π‘₯) )/tan⁑(πœ‹/4 βˆ’ π‘₯) Calculating L.H.S tan⁑〖(πœ‹/4 + π‘₯)γ€—/tan⁑〖( πœ‹/4 βˆ’π‘₯)γ€— = ((1 + π‘‘π‘Žπ‘›β‘π‘₯)/(1βˆ’ π‘‘π‘Žπ‘›β‘π‘₯ ))/((1 βˆ’ tan⁑x)/(1 + tan⁑x )) = (1 + π‘‘π‘Žπ‘›β‘π‘₯)/(1βˆ’ π‘‘π‘Žπ‘›β‘π‘₯ ) Γ— (1 + π‘‘π‘Žπ‘›β‘π‘₯)/(1βˆ’ π‘‘π‘Žπ‘›β‘π‘₯ ) = (1 + π‘‘π‘Žπ‘›β‘π‘₯ )2/((1βˆ’ π‘‘π‘Žπ‘›β‘γ€–π‘₯)2γ€— ) = R.H.S Hence proved

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