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Misc 3 - Prove 2 sin-1 3/5 = tan-1 24/7 - Chapter 2 Inverse

Misc. 3 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Misc. 3 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3
Misc. 3 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 4

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Misc 3 Prove 2 sin-1 3/5 = tan-1 24/7 We need to convert LHS in form tan-1 Converting sin-1 (πŸ‘/πŸ“) to tan-1 Let x = sin-1 (3/5) sin x = 3/5 Now, cos x = √(1βˆ’π‘ π‘–π‘›2 π‘₯) = √(1 βˆ’ (3/5)^2 ) = √(1 βˆ’ 9/25) = √((25 βˆ’ 9)/25) = √(16/25) = 4/5 Thus, tan x = sin⁑π‘₯/cos⁑π‘₯ tan x = (3/5)/(4/5) tan x = 3/4 x = tan–1 πŸ‘/πŸ’ Solving L.H.S 2 sin–1 πŸ‘/πŸ“ = 2x = 2 tan-1 (3/4) Using 2tan-1 x = tan-1 (πŸπ’™/(𝟏 βˆ’ π’™πŸ)) = tan-1 (2(3/4)/(1 βˆ’ (3/4)2)) = tan-1 ((3/2)/(1 βˆ’ 9/16)) = tan-1 ((3/2)/( (16 βˆ’ 9)/16)) = tan-1 ((3/2)/( 7/16)) = tan-1 (3/2Γ—16/7) = tan-1 (πŸπŸ’/πŸ•) = R.H.S. Hence L.H.S. = R.H.S Hence proved

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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.