Misc 3 - Chapter 3 Class 11 Trigonometric Functions
Last updated at Dec. 16, 2024 by Teachoo
Cos x + cos y formula
Sum Identities (Sum to Product Identities)
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Chapter 3 Class 11 Trigonometric Functions
Concept wise
- Radian measure - Conversion
- Arc length
- Finding Value of trignometric functions, given other functions
- Finding Value of trignometric functions, given angle
- (x + y) formula
- 2x 3x formula - Proving
- 2x 3x formula - Finding value
-
cos x + cos y formula
- 2 sin x sin y formula
- Finding Principal solutions
- Finding General Solutions
- Sine and Cosine Formula
Transcript
Misc 3 Prove that: (cos π₯ + cos y)2 + (sin π₯ β sin y)2 = 4cos2 (π₯ + y)/2 Solving LHS (ππ¨π¬β‘π+ππ¨π¬β‘π )^π + (π¬π’π§β‘πβπ¬π’π§β‘π )^π = cos2 π₯+cos2 π¦+2 cosβ‘π₯ cosβ‘π¦+sin2 π₯+ sin2 π¦ β 2sinβ‘π₯ sinβ‘π¦ = (ππππ π+ππππ π)+(ππππ π+ππππ π )+2 (cosβ‘π₯ cosβ‘π¦ βsinβ‘π₯ sinβ‘π¦) = 1 + 1 +2 (ππ¨π¬β‘π ππ¨π¬β‘πβπ¬π’π§β‘π π¬π’π§β‘π ) = 2 + 2 πππβ‘(π + π) = 2 [1 + πππβ‘(π + π) ] = 2 [1+2cos2 ((π₯ + y)/2) β 1 ] = 4 cos^2 ((π₯ + y)/2) = RH.S. Hence proved
