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Last updated at May 29, 2018 by Teachoo

Transcript

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

Changing of trignometric variables and then applying formula

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.