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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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.