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

Video TutorialsVIEW ALL [3]

Solution If sin^−1(1−x)−2sin^−1 x=π/2 then x is Concept: Basic Concepts of Trigonometric Functions.
S
The text passage contains a mathematical question involving trigonometric functions and an answer with a detailed solution process.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
HSC Arts 12th Board ExamMaharashtra State Board
Share

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

Video TutorialsVIEW ALL [3]

Solution If sin^−1(1−x)−2sin^−1 x=π/2 then x is Concept: Basic Concepts of Trigonometric Functions.
S
user
The text passage contains a mathematical question involving trigonometric functions and an answer with a detailed solution process.

TYPE: SINGLE_QUESTION_WITH_ANSWER