Ex 3.3, 22 - Prove cot x cot 2x - cot 2x cot 3x - cot 3x cot x - (x + y) formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise

Transcript

Ex 3.3, 22 Prove that cot ๐‘ฅ cot 2๐‘ฅ โ€“ cot 2๐‘ฅ cot 3๐‘ฅ โ€“ cot 3๐‘ฅ cot ๐‘ฅ = 1 Taking L.H.S. cot x cot 2x โ€“ cot 2x cot 3x โ€“ cot 3x cot x = cot x cot 2x โ€“ cot 3x (cot 2x + cot x) = cot x cot 2x โ€“ cot (2x + x) (cot 2x + cot x) = cot x cot 2x โ€“ ((cot 2x cot x โˆ’ 1)/(cot x + cot 2x)) (cot 2x + cot x) = cot x cot 2x โ€“ (cot 2x cot x โ€“ 1) = cot x cot 2x โ€“ cot 2x cot x + 1 = 1 = R.H.S. Hence L.H.S = R.H.S Hence proved

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