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JEE Main202126 Aug 2021Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

A 10 inches long pencil A B with mid point C and a small eraser P are placed on the horizontal top of a table such that P C = 5 inches and ∠ P C B = tan - 1 ( 2 ) . The acute angle through which the pencil must be rotated about C so that the perpendicular distance between eraser and pencil becomes exactly 1 inch is :

Options

  1. Atan - 1 3 4
  2. Btan - 1 1 2
  3. Ctan - 1 4 3
  4. Dtan - 1 1

Correct answer

A. tan - 1 3 4

Step-by-step solution

From figure, sin β = 1 5 tan β = 1 2 tan ( α + β ) = 2 tan α + β = tan α + 1 2 1 - tan α   . 1 2 = 2 α = tan - 1 3 4

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