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Prove that: tan^−1 1/5+tan^−1 1/7+tan^−1 1/3+tan^−1 1/8=π/4 - CBSE (Science) Class 12 - Mathematics

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Question

 

Prove that:

`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`

 

Solution

 

LHS:

 `(tan^(-1)""1/5+tan^(-1)""1/7)+(tan^(-1)""1/3+tan^(-1)""1/8)`

`=tan^(-1)((1/5+1/7)/(1-1/5xx1/7))+tan^(-1)((1/3+1/8)/(1-1/3xx1/8)) [:.tan^(-1)A+tan^(-1)B=tan^(-1)((A+B)/(1-AB))] `          

`=tan^(-1)""6/17+tan^(-1)""11/23`

`=tan^(-1)((6/17+11/23)/(1-6/17xx11/23))`

`=tan^(-1)(325/325)`

`=tan^(-1) 1`

`=pi/4`

 
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Solution Prove that: tan^−1 1/5+tan^−1 1/7+tan^−1 1/3+tan^−1 1/8=π/4 Concept: Properties of Inverse Trigonometric Functions.
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