Question

if tan(x-y) .tan(x+y)=1 then find the value of tan(4x/3) ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The answer is $\sqrt{3}$

Given: tan(x-y). tan(x+y) = 1

To find: The value of tan (4x/3)  

Solution:

From given data

⇒ tan(x-y). tan(x+y) = 1

⇒  $tan(x-y) = \frac{1}{tan(x+y)}$    

⇒  $tan(x-y) = cot (x+y)}$    [  $\frac{1}{tanA} = cot A$ ]

⇒  $tan(x-y) =tan (90 - (x+y))}$   [ tan (90 - A) = cot A ]

⇒  x - y = 90 - (x+y)

⇒  x - y = 90 - x -y

⇒  2x = 90  

⇒   x = 45°

⇒ $tan \frac{4x}{3}$  =  $tan \frac{4(45)}{3}$

= $tan 4(15)$  = tan 60°  = $\sqrt{3}$  

Therefore, $tan \frac{4x}{3}$ = $\sqrt{3}$  

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