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Ex 3.3, 18 - Chapter 3 Class 11 Trigonometric Functions

Last updated at May 29, 2023 by

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

Ex 3.3, 18 - Chapter 3 Class 11 Trigonometric Functions - Part 2

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Ex 3.3, 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 ) = 〖2 𝑐𝑜𝑠((𝑥 + 𝑦 )/2)〗⁡〖 𝑠𝑖𝑛⁡((𝑥 − 𝑦 )/2) 〗/(2 𝑐𝑜𝑠⁡((𝑥 + 𝑦 )/2) 𝑐𝑜𝑠⁡((𝑥 − 𝑦 )/2) ) 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 − 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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