Misc 6 - Prove cos-1 12/13 + sin-1 3/5 = sin-1 56/65 - Miscellaneous

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Misc 6 Prove  cos-1 12/13 + sin-1 3/5 = sin-1 56/65 Let a = cos-1 12/13 & b = sin-1 3/5 We know that sin (a + b) = sin a cos b + cos a sin b sin (a + b) = 5/13 × 4/5 + 12/13 × 3/5 = 20/65 + 36/65 = 56/65 ∴ sin (a + b) = 56/65 ⇒ a + b = sin-1 56/65 Putting values cos-1 12/13 + sin-1 3/5 = sin-1 56/65 Hence L.H.S = R.H.S Hence Proved

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