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Example 26 - Prove cos 2x cos x/2 - cos 3x cos 9x/2 = sin 5x - 2 sin x sin y formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Example 26 Prove that cos 2x cos ๐‘ฅ/2 โ€“ cos 3x cos 9๐‘ฅ/2 = sin 5x sin 5๐‘ฅ/2 Taking L.H.S Now, cos 2x cos ๐‘ฅ/2 โ€“ cos 3x cos 9๐‘ฅ/2 Putting values = 1/2 ("cos " (5x/2)" + cos " (3x/2)) โ€“ 1/2 ("cos " (15๐‘ฅ/2)" + cos " ((โˆ’3๐‘ฅ)/2)) = 1/2 ("cos " (5x/2)" + cos " (3x/2)) โ€“ 1/2 ("cos " (15๐‘ฅ/2)" + cos " (3๐‘ฅ/2)) = 1/2 ("cos " (5x/2)" + cos " (3x/2)"โ€“ cos " (15๐‘ฅ/2)"โ€“ cos " (3๐‘ฅ/2)) = 1/2 ("cos " (5x/2)"โ€“ cos " (15๐‘ฅ/2)"+ cos " (3x/2)"โ€“ cos " (3๐‘ฅ/2)) = 1/2 ("cos " (5x/2)"โ€“ cos " (15๐‘ฅ/2)"+ " 0) = 1/2 ("cos " (5x/2)"โ€“ cos " (15๐‘ฅ/2)) = 1/2 ("โ€“ 2 sin " ((5๐‘ฅ/2 +15/2 ๐‘ฅ)/2)" . sin " ((5๐‘ฅ/2 โˆ’ 15/2 ๐‘ฅ)/2)) = 1/2 ("โ€“ 2 sin " ((5๐‘ฅ + 15๐‘ฅ)/(2 ร— 2))" . sin " ((5๐‘ฅ โˆ’ 15๐‘ฅ)/(2 ร— 2))) = 1/2 ("โ€“ 2 sin " (20๐‘ฅ/4)" . sin " (( โˆ’10๐‘ฅ)/4)) = 1/2 ("โ€“ 2 sin " (5๐‘ฅ)" . sin " (( โˆ’5๐‘ฅ)/2)) = 1/2 ("โ€“ 2 sin " (5๐‘ฅ)" ร— " (โˆ’ "sin " (( 5๐‘ฅ)/2))) = 1/2 ("2 sin " (5๐‘ฅ)" sin " (( 5๐‘ฅ)/2)) = sin (5๐‘ฅ) sin (( 5๐‘ฅ)/2) = R.H.S Hence L.H.S. = R.H.S. Hence proved

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