Misc 3 - Chapter 3 Class 11 Trigonometric Functions

Last updated at Dec. 16, 2024 by Teachoo

Next: Misc 4 Important → Go Ad-free

Transcript

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

Made by

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

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular