Misc 3 - Chapter 3 Class 11 Trigonometric Functions

Last updated at April 16, 2024 by Teachoo

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Misc 3 Prove that: (cos 𝑥 + cos y)2 + (sin 𝑥 – sin y)2 = 4cos2 (𝑥 + y)/2 Solving LHS (𝐜𝐨𝐬⁡𝒙+𝐜𝐨𝐬⁡𝒚 )^𝟐 + (𝐬𝐢𝐧⁡𝒙–𝐬𝐢𝐧⁡𝒚 )^𝟐 = cos2 𝑥+cos2 𝑦+2 cos⁡𝑥 cos⁡𝑦+sin2 𝑥+ sin2 𝑦 – 2sin⁡𝑥 sin⁡𝑦 = (𝒄𝒐𝒔𝟐 𝒙+𝒔𝒊𝒏𝟐 𝒙)+(𝒄𝒐𝒔𝟐 𝒚+𝒔𝒊𝒏𝟐 𝒚 )+2 (cos⁡𝑥 cos⁡𝑦 –sin⁡𝑥 sin⁡𝑦) = 1 + 1 +2 (𝐜𝐨𝐬⁡𝒙 𝐜𝐨𝐬⁡𝒚–𝐬𝐢𝐧⁡𝒙 𝐬𝐢𝐧⁡𝒚 ) = 2 + 2 𝒄𝒐𝒔⁡(𝒙 + 𝒚) = 2 [1 + 𝒄𝒐𝒔⁡(𝒙 + 𝒚) ] = 2 [1+2cos2 ((𝑥 + y)/2) – 1 ] = 4 cos^2 ((𝑥 + y)/2) = RH.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 and Computer Science at Teachoo

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