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# Prove 2 Tan^(-1) 1/2 + Tan^(-1) 1/7 = Tan^(-1) 31/17 - CBSE (Commerce) Class 12 - Mathematics

ConceptProperties of Inverse Trigonometric Functions

#### Question

Prove 2 tan^(-1)  1/2 + tan^(-1)  1/7 = tan^(-1)  31/17

#### Solution

Tp prove 2 tan^(-1)  1/2 + tan^(-1)  1/7 = tan^(-1)  31/17

L.H.S = 2tan^(-1)  1/2 + tan^(-1)  1/7

= tan^(-1)   (2. 1/2)/(1-(1/2)^2) + tan^(-1)  1/7      "                   "[2 tan^(-1) x = tan^(-1)  (2x)/(1-x^2)]

= tan^(-1)  1/ ((3/4)) + tan^(-1)  1/7

= tan^(-1)  4/3 + tan^(-1)  1/7

= tan^(-1)  (4/3 + 1/7) /(1 - 4/3. 1/7)  [tan^(-1) x + tan^(-1) y = tan^(-1)  (x + y)/(1 -  xy)]

= tan^(-1)  ((28+3)/21)/((21-4)/21)

= tan^(-1)  31/17 = R.H.S

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 2: Inverse Trigonometric Functions
Q: 4 | Page no. 47
Solution Prove 2 Tan^(-1) 1/2 + Tan^(-1) 1/7 = Tan^(-1) 31/17 Concept: Properties of Inverse Trigonometric Functions.
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