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Misc 3 - Prove (cos x + cos y)2 + (sin x - sin y)2 - Class 11 - cos x + cos y formula

Misc 3 - Chapter 3 Class 11 Trigonometric Functions - Part 2

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Misc 3 Prove that: (cos x + cos y)2 + (sin x – sin y)2 = 4 cos2 (x + y)/2 Taking L.H.S (cos x + cos y )2 + (sin x – sin y )2 = ("2cos (" (π‘₯ + 𝑦)/2 ") cos (" (π‘₯ βˆ’ 𝑦)/2 ")" )^2 + ("2 cos (" (π‘₯ + 𝑦)/2 ") sin (" (π‘₯ βˆ’ 𝑦)/2 ")" )^2 = ("22 cos2 (" (π‘₯ + 𝑦)/2 ") cos2 (" (π‘₯ βˆ’ 𝑦)/2 ")" ) + ("22 cos2 (" (π‘₯ + 𝑦)/2 ") sin2 (" (π‘₯ βˆ’ 𝑦)/2 ")" ) = 4 cos2 ((π‘₯ + 𝑦)/2) . cos2 ((π‘₯ βˆ’ 𝑦)/2) + 4 cos2 ((π‘₯ + 𝑦)/2) sin2 ((π‘₯ βˆ’ 𝑦)/2) = 4cos2 ( (π‘₯ + 𝑦)/2) ("cos2 ( " (π‘₯ βˆ’ 𝑦)/2 ") + sin2 ( " (π‘₯ βˆ’ 𝑦)/2 ")" ) = 4 cos2 ( (π‘₯ + 𝑦)/2) Γ— 1 = 4 cos2 ( (π‘₯ + 𝑦)/2) = R.H.S. Hence , L.H.S.= R.H.S. Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.