
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Cos x + cos y formula
Ex 3.3, 11 Important
Misc 3 You are here
Misc 4 Important
Ex 3.3, 14
Ex 3.3, 15
Misc 5
Misc 7 Important
Example 16 Important
Ex 3.3, 16 Important
Ex 3.3, 17
Ex 3.3, 18 Important
Ex 3.3, 19
Ex 3.3, 20
Ex 3.3, 21 Important
Example 17 Important
Misc 6 Important
cos x + cos y formula
Last updated at May 29, 2023 by Teachoo
Misc 3 Prove that: (cos x + cos y)2 + (sin x β sin y)2 = 4 cos2 (x + y)/2 Taking L.H.S (cos x + cos y )2 + (sin x β sin y )2 = ("2cos (" (π₯ + π¦)/2 ") cos (" (π₯ β π¦)/2 ")" )^2 + ("2 cos (" (π₯ + π¦)/2 ") sin (" (π₯ β π¦)/2 ")" )^2 = ("22 cos2 (" (π₯ + π¦)/2 ") cos2 (" (π₯ β π¦)/2 ")" ) + ("22 cos2 (" (π₯ + π¦)/2 ") sin2 (" (π₯ β π¦)/2 ")" ) = 4 cos2 ((π₯ + π¦)/2) . cos2 ((π₯ β π¦)/2) + 4 cos2 ((π₯ + π¦)/2) sin2 ((π₯ β π¦)/2) = 4cos2 ( (π₯ + π¦)/2) ("cos2 ( " (π₯ β π¦)/2 ") + sin2 ( " (π₯ β π¦)/2 ")" ) = 4 cos2 ( (π₯ + π¦)/2) Γ 1 = 4 cos2 ( (π₯ + π¦)/2) = R.H.S. Hence , L.H.S.= R.H.S. Hence proved