Cos x + cos y formula

Chapter 3 Class 11 Trigonometric Functions
Concept wise

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### Transcript

Example 16 Prove that πππ β‘γ7π₯ + πππ β‘5π₯ γ/π ππβ‘γ7π₯ β π ππβ‘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 γπππ  γβ‘γ7π₯ + πππ β‘5π₯ γ/π ππβ‘γ7π₯ β π ππβ‘5π₯ γ = (2 γ πππ  γβ‘γ6x πππ β‘π₯ γ)/(2 πππ β‘γ 6π₯ siπβ‘π₯ γ ) = πππ β‘γ π₯γ/π ππβ‘γ π₯γ = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.