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


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Misc 5 Prove cos-1 4/5 + cos-1 12/13 = cos-1 33/65 Let a = cos-1 4/5 and b = cos-1 12/13 Finding sin a, cos a Let a = cos-1 4/5 cos a = 4/5 We know that sin a = √(1 βˆ’cos^2β‘π‘Ž ) =√(1βˆ’(4/5)^2 ) " =" √(9/25) "=" 3/5 Finding sin b, cos b Let b = cos-1 12/13 cos b = 12/13 We know that sin b = √(1 βˆ’π‘π‘œπ‘ 2 𝑏) = √(1 βˆ’(12/13)^2 ) = √(25/169) = 5/13 Now, cos (a + b) = cos a cos b – sin a sin b cos (a + b) = 4/5 Γ— 12/13 – 3/5 Γ— 5/13 = 48/65 βˆ’ 3/13 = (48 βˆ’ 3(5))/65 = (48 βˆ’ 15)/65 = πŸ‘πŸ‘/πŸ”πŸ“ Putting cos a = 4/5 , sin a = 3/5 & cos b = 12/13 , sin b = 5/13 Thus, cos (a + b) = 33/65 a + b = cos-1 (33/65) Putting a = cos-1 4/5 & b = cos-1 12/15 cos-1 πŸ’/πŸ“ + cos-1 𝟏𝟐/πŸπŸ“ = cos-1 πŸ‘πŸ‘/πŸ”πŸ“ Which is what we had to prove 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.