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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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Transcript

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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.