Cos x + cos y formula

Chapter 3 Class 11 Trigonometric Functions
Concept wise

Transcript

Misc 5 Prove that: sin ๐ฅ + sin 3๐ฅ + sin5๐ฅ + sin 7๐ฅ = 4cos ๐ฅ cos 2๐ฅ sin 4๐ฅ Solving LHS sin ๐ฅ + sin 3๐ฅ + sin5๐ฅ + sin 7๐ฅ = (๐ฌ๐ข๐งโก๐+๐๐๐ ๐๐)+(๐ฌ๐ข๐งโก๐๐+๐๐๐โก๐๐) = 2 sin ((๐ฅ + 5๐ฅ)/2) .cos ((๐ฅ โ 5๐ฅ)/2) + 2sin ((3๐ฅ + 7๐ฅ)/2) cos ((3๐ฅ โ 7๐ฅ)/2) = 2 sin 3๐ฅ cos (โ2๐ฅ) + 2sin 5๐ฅ cos (โ2๐ฅ) = 2 sin 3๐ฅ cos 2๐ฅ + 2sin 5๐ฅ cos 2๐ฅ = 2 cos 2๐ฅ [ sin 3๐ฅ + sin 5๐ฅ] = 2cos 2๐ฅ ("2sin " ((3๐ฅ + 5๐ฅ)/2)" . cos" ((3๐ฅ โ 5๐ฅ)/2)) = 2cosโก2๐ฅ [2 sinโก4๐ฅ.cosโกใ(โ๐ฅ)ใ] = ๐ ๐๐จ๐ฌโก๐๐ ๐ฌ๐ข๐งโก๐๐ ๐๐จ๐ฌโก๐ = RH.S. = 2 cos 2๐ฅ [ sin 3๐ฅ + sin 5๐ฅ] = 2cos 2๐ฅ ("2sin " ((3๐ฅ + 5๐ฅ)/2)" . cos" ((3๐ฅ โ 5๐ฅ)/2)) = 2cosโก2๐ฅ [2 sinโก4๐ฅ.๐๐จ๐ฌโกใ(โ๐)ใ] = ๐ ๐๐จ๐ฌโก๐๐ ๐ฌ๐ข๐งโก๐๐ ๐๐จ๐ฌโก๐ = RH.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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.