Ex 3.3, 18 - Prove sin x - sin⁡ y /cos x + cos y = tan (x - y)/2 - cos x + cos y formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex3.3, 18 Prove that 〖sin x − 〗⁡sin⁡y /(𝑐𝑜𝑠⁡x + 𝑐𝑜𝑠⁡y ) = tan (x − y)/2 Solving L.H.S 〖sin x − 〗⁡sin⁡y /(𝑐𝑜𝑠⁡x + 𝑐𝑜𝑠⁡y ) We Know that sin x – sin y = 2 cos ( (𝑥 + 𝑦 )/2) sin ( (𝑥 − 𝑦 )/2) & cos x + cos y = 2 cos ( (𝑥 + 𝑦 )/2) cos ( (𝑥 − 𝑦 )/2) 〖sin x − 〗⁡sin⁡y /(𝑐𝑜𝑠⁡x + 𝑐𝑜𝑠⁡y ) = 〖2 𝑐𝑜𝑠 ((𝑥 + 𝑦)/2)〗⁡〖 𝑠𝑖𝑛⁡〖 ((𝑥 − 𝑦)/2)〗 〗/(2 𝑐𝑜𝑠⁡〖 ((𝑥 + 𝑦)/2)〗 𝑐𝑜𝑠⁡〖 ((𝑥 − 𝑦)/2)〗 ) = 𝑠𝑖𝑛⁡〖" " ((𝑥 − 𝑦 )/2)〗/(𝑐𝑜𝑠⁡〖 ((𝑥 − 𝑦)/2)〗 ) = tan (𝑥 − 𝑦 )/2 = R.H.S Hence L.H.S. = R.H.S. Hence proved

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