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Misc 3 - Chapter 3 Class 11 Trigonometric Functions

Last updated at May 29, 2023 by

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 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.