Misc 17 - Solve tan-1 (x/y) - tan-1 (x - y)/(x + y) - Miscellaneous

  1. Class 12
  2. Important Question for exams Class 12

Transcript

Misc 17 Solve tan-1 (x/y) tan-1 (x y)/(x + y) is equal to (A) /2 (B) /3 (C) /4 (D) ( 3 )/4 We know that tan 1 x tan 1 y = tan 1 (( )/( + )) tan-1 x/y tan-1 ((x y)/(x + y)) = tan-1 [(x/y (x y )/(x + y))/(1 + (x/y) ((x y )/(x + y)) )] = tan-1 ((( ( + ) ( ))/( ( + ) ))/(( ( + )+ ( ))/( ( + ) ))) = tan-1 (( ( + ) ( ))/( ( + ) ) ( ( + ))/( ( + )+ ( ) )) = tan-1 (( ( + ) ( ))/( ( + ) + ( + )) ( ( + ))/( ( + ) )) = tan-1 (( ( + ) ( ))/( ( + ) + ( + ))) = tan-1 (( 2+ + 2)/( + 2 + 2 ))) = tan-1 (( 2+ 2+ )/( 2 + 2 + ))) = tan-1 (( 2+ 2 + 0)/( 2 + 2 + 0)) = tan-1 (( 2+ 2 )/( 2 + 2 )) = tan-1 (1) = tan-1 (tan /4) = /4 Hence, correct answer is C

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