Example 13 - Prove sin (x+y) / sin (x-y) = tan x + tan y - Examples

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Example 13 - Chapter 3 Class 11 Trigonometric Functions - NCERT Prove that sin⁡〖(𝑥+𝑦) 〗/sin⁡〖(𝑥−𝑦) 〗 = tan⁡〖𝑥 + tan⁡𝑦 〗/tan⁡〖𝑥 −tan⁡𝑦 〗 L.H.S. sin⁡〖( 𝑥 + 𝑦)〗/sin⁡〖( 𝑥 − 𝑦)〗 = (sin⁡𝑥 cos⁡𝑦 + 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/(sin⁡𝑥 cos⁡𝑦 − 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦 ) R.H.S. tan⁡〖𝑥 + tan⁡𝑦 〗/(tan⁡𝑥 − tan⁡𝑦 ) = (sin⁡𝑥/cos⁡𝑥 + sin⁡𝑦/cos⁡𝑦 )/(sin⁡𝑥/cos⁡𝑥 − sin⁡𝑦/cos⁡𝑦 ) = ((sin⁡𝑥 cos⁡𝑦 + 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/cos⁡〖𝑥 cos⁡𝑦 〗 )/((sin⁡𝑥 cos⁡𝑦 − 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/cos⁡〖𝑥 cos⁡𝑦 〗 ) = (sin⁡𝑥 cos⁡𝑦 + 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/(sin⁡𝑥 cos⁡𝑦 − 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦 ) = L.H.S Hence L.H.S = R.H.S Hence proved

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