HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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# Solution for If tan−1((x−1)/(x−2))+cot−1((x+2)/(x+1))=π4; - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

ConceptBasic Concepts of Trigonometric Functions

#### Question

If tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4;

#### Solution

"Given ",tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4

tan^-1((x-1)/(x-2))+tan^-1((x+1)/(x+2))=pi/4;

tan^-1((x-1)/(x-2))=pi/4-tan^-1((x+1)/(x+2))

=tan^-1(1)-tan^-1((x+1)/(x+2))

=tan^-1[(1-(x+1)/(x+2))/(1+(x+1)/(x+2))]  ........[because tan^-1x-tan^-1y=tan^-1((x-y)/(1+xy))]

=tan^-1[(x+2-x-1)/(x+2+x+1)]

tan^-1((x-1)/(x-2))=tan^-1(1/(2x+3))

(x-1)/(x-2)=1/(2x+3)

(x-1)(2x+3)=x-2

2x^2-1=0

2x^2=1

x^2=1/2

x=+-1/sqrt2

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#### APPEARS IN

2014-2015 (October) (with solutions)
Question 3.2.3 | 4.00 marks

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Solution If tan−1((x−1)/(x−2))+cot−1((x+2)/(x+1))=π4; Concept: Basic Concepts of Trigonometric Functions.
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