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Prove `Tan^(-1) 2/11 + Tan^(-1) 7/24 = Tan^(-1) 1/2` - Mathematics

Prove `tan^(-1)  2/11 + tan^(-1)  7/24 = tan^(-1)  1/2`

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Solution

To prove:  `tan^(-1)  2/11 + tan^(-1)  7/24 = tan^(-1)  1/2`

L.H.S =` tan^(-1)  2/11 + tan^(-1)  7/24`

`= tan^(-1) (2/11 + 7/24)/(1-2/11. 7/24)`    `[tan^(-1) x + tan^(-1) y = tan^(-1)  (x + y)/(1 - xy)]`

= tan^(-1)  `((48+77)/(11xx24))/((11xx24 - 14)/(11xx24))`

`= tan^(-1)  (48 + 77)/(264 - 14) = tan^(-1)  125/250 = tan^(-1)  1/2 =`  R.H.S

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APPEARS IN

NCERT Class 12 Maths
Chapter 2 Inverse Trigonometric Functions
Q 3 | Page 47
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