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

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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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