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Misc 4 - Chapter 3 Class 11 Trigonometric Functions
Last updated at May 29, 2023 by Teachoo
Cos x + cos y formula
Sum Identities (Sum to Product Identities)
Ex 3.3, 11 Important
Misc 3
Misc 4 Important You are here
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
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 4 Prove that: (cos x – cos y)2 + (sin x – sin y)2 = 4 sin2 (x − y)/2 Solving L.H.S (cos x – cos y )2 + (sin x – sin y )2 = (−"2 sin " ((𝑥 + 𝑦)/2)" sin " ((𝑥 − 𝑦)/2))^2 + ("2 cos " ((𝑥 + 𝑦)/2)" sin " ((𝑥 − 𝑦)/2))^2 = ((−"2)2 sin2 " ((𝑥 + 𝑦)/2)" sin2 " ((𝑥 − 𝑦)/2)) + ("22 cos2 " ((𝑥 + 𝑦)/2)" sin2 " ((𝑥 − 𝑦)/2)) = 4 sin2 ((𝑥 + 𝑦)/2) . sin2 ((𝑥 − 𝑦)/2) + 4 cos2 ((𝑥 + 𝑦)/2) sin2 ((𝑥 − 𝑦)/2) We know that cos x – cos y = –2 sin ((𝑥 + 𝑦)/2) sin ((𝑥 − 𝑦)/2) sin x – sin y = 2cos ((𝑥 + 𝑦)/2) sin ((𝑥 − 𝑦)/2) We know that sin2 x + cos2 x = 1 Replace x by ((𝑥 + 𝑦)/2) sin2 ((x + y)/2) + cos2 ((x + y)/2) = 1 = 4 sin2 ((𝑥 − 𝑦)/2) ("sin2 " ((𝑥 + 𝑦)/2)" + cos2 " ((𝑥+ 𝑦)/2)) = 4 sin2 ((𝑥 − 𝑦)/2) × 1 = 4 sin2 ((𝑥 − 𝑦)/2) = R.H.S. Hence , L.H.S.= R.H.S. Hence proved
