Misc 5 - Prove cos-1 4/5 + cos-1 12/13 = cos-1 33/65 - Changing of trignometric variables and then applying formula

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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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 We know that cos (a + b) = cos a cos b sin a sin b cos (a + b) = 4/5 12/13 3/5 5/13 = 48/65 - 3/13 = (48 3(5))/65 = (48 15)/65 = 33/65 cos (a + b) = 33/65 a + b = cos-1 (33/65) cos-1 4/5 + cos-1 12/15 = cos-1 33/65 Hence L.H.S = R.H.S Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.