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# Solution - If sin^−1(1−x)−2sin^−1 x=π/2 then x is - HSC Science (Computer Science) 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 marks

#### Reference Material

Solution for question: If sin^−1(1−x)−2sin^−1 x=π/2 then x is concept: Basic Concepts of Trigonometric Functions. For the courses HSC Science (Computer Science), HSC Science (General) , HSC Science (Electronics), HSC Arts
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