Misc. 3 - Chapter 2 Class 12 Inverse Trigonometric Functions

Transcript

Misc 3 Prove 2 sin-1 3/5 = tan-1 24/7 We need to convert LHS in form tan-1 Let first calculate sin-1 ( / ) Let x = sin-1 (3/5) sin x = 3/5 cos x = (1 2 ) = (1 (3/5)^2 ) = (1 9/25) = ((25 9)/25) = (16/25) = 4/5 tan x = sin /cos = (3/5)/(4/5) = 3/4 tan x = 3/4 x = tan 1 3/4 Taking L.H.S 2 sin-1 3/5 = 2x = 2 tan-1 (3/4) Using 2tan-1 x = tan-1 ( /( )) = tan-1 (2(3/4)/(1 (3/4)2)) = tan-1 ((3/2)/(1 9/16)) = tan-1 ((3/2)/( (16 9)/16)) = tan-1 ((3/2)/( 7/16)) = tan-1 (3/2 16/7) = tan-1 (24/7) = R.H.S. Hence L.H.S. = R.H.S Hence proved