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Misc 5 - ProveΒ cos-1 4/5 + cos-1 12/13 = cos-1 33/65 - Miscellaneous

Misc. 5 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Misc. 5 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

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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 We use cos (a + b) formula 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.