Last updated at May 29, 2018 by Teachoo

Transcript

Misc 4 Prove that: (cos x – cos y)2 + (sin x – sin y)2 = 4 sin2 (x − y)/2 Taking L.H.S (cos x – cos y )2 + (sin x – sin y )2 = (−"2 sin (" (𝑥 + 𝑦)/2 ") sin (" (𝑥 − 𝑦)/2 ")" )^2 + ("2 cos (" (𝑥 + 𝑦)/2 ") sin (" (𝑥 − 𝑦)/2 ")" )^2 = ((−"2)2 sin2 (" (𝑥 + 𝑦)/2 ") sin2 (" (𝑥 − 𝑦)/2 ")" ) + ("22 cos2 (" (𝑥 + 𝑦)/2 ") sin2 (" (𝑥 − 𝑦)/2 ")" ) = 4 sin2 ((𝑥 + 𝑦)/2) . sin2 ((𝑥 − 𝑦)/2) + 4 cos2 ((𝑥 + 𝑦)/2) sin2 ((𝑥 − 𝑦)/2) = 4 sin2 ( (𝑥 − 𝑦)/2) ("sin2 ( " (𝑥 + 𝑦)/2 ") + cos2 ( " (𝑥+ 𝑦)/2 ")" ) = 4 sin2 ( (𝑥 − 𝑦)/2) × 1 = 4 sin2 ( (𝑥 − 𝑦)/2) = R.H.S. Hence , L.H.S.= R.H.S. Hence proved

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.