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# If tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4 ,find the value of x - CBSE (Commerce) Class 12 - Mathematics

ConceptInverse Trigonometric Functions (Simplification and Examples)

#### Question

If tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4 ,find the value of x

#### Solution

Given that

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

Taking LHS, we get:

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

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

=tan^(-1)([((x-2)(x+4)(x+2)(x-4))/(x^2-16-(x^2-4))])

=tan^(-1)[(x^2+2x-8+x^2-2x-8)/(12)]

=tan^(-1)[(2x^2-16)/(-12)]

hence

tan^(-1)[(2x^2-16)/(-12)]=pi/4

[(2x^2-16)/(-12)]=tan (pi/4)

=>(x^2-8)/(-6)=1

=>x^2-8=-6

=>x^2=2

=>x=+-2

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Solution If tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4 ,find the value of x Concept: Inverse Trigonometric Functions (Simplification and Examples).
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