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

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

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

  1. Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)
  2. Concept wise

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.