Ex 3.3, 17 - Chapter 3 Class 11 Trigonometric Functions
Last updated at April 16, 2024 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
Ex 3.3, 16 Important
Ex 3.3, 17 You are here
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
Ex 3.3, 17 Prove that ๐ ๐๐โกใ5๐ฅ + ๐ ๐๐โก3๐ฅ ใ/๐๐๐ โกใ5๐ฅ + ๐๐๐ โก3๐ฅ ใ = tan 4x Solving L.H.S. ๐ ๐๐โกใ5๐ฅ + ๐ ๐๐โก3๐ฅ ใ/๐๐๐ โกใ5๐ฅ + ๐๐๐ โก3๐ฅ ใ We solve sin 5x + sin 3x & cos 5x + cos 3x seperately sin 5x + sin 3x = 2 sin ((5x+3x)/2) cos ((5xโ3x)/2) = 2 sin (8๐ฅ/2) cos (2๐ฅ/2) = 2 sin 4x cos x cos 5x + cos 3x = 2 cos ((5x+3x)/2) cos ((5xโ3x)/2) = 2 cos (8๐ฅ/2) cos (2๐ฅ/2) = 2 cos 4x cos (x) Now ๐๐๐โกใ๐๐ + ๐๐๐โก๐๐ ใ/๐๐๐โกใ๐๐ + ๐๐๐โก๐๐ ใ = (2 ใ ๐ ๐๐ ใโกใ4x ๐๐๐ โก๐ฅ ใ)/(2 ๐๐๐ โกใ 4๐ฅ ๐๐๐ โก๐ฅ ใ ) = ๐๐๐โกใ ๐๐ใ/๐๐จ๐ฌโกใ ๐๐ใ = tan 4x = R.H.S Hence L.H.S = R.H.S Hence proved
