Question

Tan (a+b)=√3
Tan (a-b)=1
Find the value of a and b

Answer 1

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HERE IS YOUR ANSWER.............

Plz refer the solution➡➡➡➡

Answer 2

Answer :

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$a = \frac{105}{2} \: and \: b \: = \frac{15}{2}$

Solution :

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$\tan(a + b) = \sqrt{3} .....(1) \\ \\ \tan(a - b) = 1$

As we know that :

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${ \tan }^{ - 1} \sqrt{3} = 60 \\ \\ and \: { \tan}^{ - 1} 1 = 45$

Now, from equation (1) and (2) :

$(a + b )= { \tan }^{ - 1} \sqrt{3} ....(1) \\ \\ ( a - b) = { \tan}^{ - 1} 1....(2)$

$a + b= 60....(3) \\ \\ a - b = 45....(4)$

On adding equation (3) and (4) :

$2a = 105 \\ \\ = > a = \frac{105}{2}$

On putting the value of 'a' in equation (3):

$\frac{105}{2} + b = 60 \\ \\ = > b = 60 - \frac{105}{2} = \frac{120 - 105}{2} \\ \\ = > b = \frac{15}{2}$