text: HSC Arts 12th Board ExamMaharashtra State Board
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  If sin^−1(1−x)−2sin^−1 x=π/2 then x is - HSC Arts 12th Board Exam - Mathematics and Statistics
  
  ConceptBasic Concepts of Trigonometric Functions
  
  Question
  
  If sin^-1(1-x) -2sin^-1x = pi/2 then x is
  
  1. -1/2
  2. 1
  3. 0
  4. 1/2
  
  Solution
  
  (c)
  
  sin^-1(1-x)-2sin^-1x=pi/2
  
  sin^-1(1-x)=pi/2+2sin^-1x
  
  (1-x)=sin(pi/2+2sin^-1x)
  
  (1-x)=cos(2sin^-1x)
  
  (1-x)=cos(cos^-1(1-2x^2))
  
  (1-x)=1-2x^2
  
  2x^2-x=0
  
  x(2x-1)=0
  
  x=0 or 2x-1=0
  
  x=0 or x=1/2
  
  "for "x =1/2
  
  sin^-1(1-x)-2sin^-1x=sin^-1(1/2)-2sin^-1(1/2)=-sin^-1(1/2)=pi/6
  
  So x=1/2 is not solution of the given equation
  
  for x=0
  
  sin^-1(1-x)-2sin^-1x=sin^-1(1)-2sin^-1(0)=pi/2-0=pi/2
  
  So x = 0 is a valid solution of the given equation.
  
  Is there an error in this question or solution?
  
  APPEARS IN
  
  2015-2016 (March) (with solutions)
  Question 1.1.2 | 2.00 marks
  
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  Solution If sin^−1(1−x)−2sin^−1 x=π/2 then x is Concept: Basic Concepts of Trigonometric Functions.
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