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Example 16 - 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
Ex 3.3, 14
Ex 3.3, 15
Misc 5
Misc 7 Important
Example 16 Important You are here
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
Example 16 Prove that πππ β‘γ7π₯ + πππ β‘5π₯ γ/π ππβ‘γ7π₯ β π ππβ‘5π₯ γ = cot x Taking L.H.S. We solve cos 7x + cos 5x & sin 7x β sin 5x separately cos x + cos y = 2 cos (π₯ + π¦)/2 cos (π₯ β π¦)/2 Putting x = 7x & y = 5x cos 7x + cos 5x = 2 cos ((7π₯ + 5π₯)/2) cos ((7π₯ β 5π₯)/2) = 2 cos (12π₯/2) cos (2π₯/2) = 2 cos 6x cos x sin x β sin y = 2 cos (π₯ + π¦)/2 sin (π₯ β π¦)/2 Putting x = 7x & y = 5x sin 7x β sin 5x = 2 cos ((7π₯ + 5π₯)/2) sin((7π₯ β 5π₯)/2) = 2 cos (12π₯/2) sin (2π₯/2) = 2 cos 6x sin x Now γπππ γβ‘γ7π₯ + πππ β‘5π₯ γ/π ππβ‘γ7π₯ β π ππβ‘5π₯ γ = (2 γ πππ γβ‘γ6x πππ β‘π₯ γ)/(2 πππ β‘γ 6π₯ siπβ‘π₯ γ ) = πππ β‘γ π₯γ/π ππβ‘γ π₯γ = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved
