Misc 3 - Chapter 3 Class 11 Trigonometric Functions

Last updated at June 22, 2023 by Teachoo

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

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

Next: Misc 4 Important → Ask a doubt

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular