Question

if tan(A+B)=1 AND tan(A-B)=1/ROOT3 THEN FIMD A AND B​

Answer 1

Tan ( A + B ) = 1

So.. Tan ( A + B ) = Tan 45°

By Comparing , A + B = 45_@1

Now , Tan ( A - B ) = 1/√3

So.. Tan ( A - B ) = Tan 30°

By Comparing , A - B = 30_@2

From @1 & @2 ( On adding )

We get A = 37.5°

And B= 7.5°

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Answer 2

The value of ∠A and ∠B are 37.5° and 7.5°.

Step-by-step explanation:

We have,

$\tan (A+B)=1$ and $\tan (A-B)=\dfrac{1}{\sqrt{3}}$

To find, ∠A and ∠B = ?

$\tan (A+B)=1=\tan 45$

⇒ A + B = 45°       ....(1)

$\tan (A-B)=\dfrac{1}{\sqrt{3}} =\tan 30$

⇒ A - B = 30°       ....(2)

On adding (1) and (2), we get

2A = 75°

⇒ A = $\dfrac{75}{2}$=37.5°  

Putting the value of A in (1), we get

37.5° + B = 45°

⇒ B = 45° - 37.5° = 7.5°

∴ ∠A = 37.5° and ∠B = 7.5°

Hence, the value of ∠A and ∠B are 37.5° and 7.5°.