Question

if tan(A+B)= 1/root 3 and tan (A-B)=root 3 , 0 degree B then find A AND B

Answer 1

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Given that,

• tan (A + B) = 1/√3
• tan (A - B) = √3

To Find,

• Values of A & B

We know that,

☯ tan 30 ° = 1/√3

• A + B = 30° ..... (1)

☯ tan 60° = √3

• A - B = 60° ..... (2)

Subtract the equations (1) & (2)

A + B = 30°

A - B = 60°

(-) (+) (-)

--------------------------

2B = - 30

--------------------------

➡ 2B = - 30

➡ B = -30/2

➡ B = - 15

$\boxed{∴ B = - 15°}$

Substitute the value of B in (1)

➡ A + (- 15) = 30

➡ A - 15 = 30

➡ A = 30 + 15

➡ A = 45

$\boxed{∴ A = 45° }$

$\underline{\boxed{\bf{\purple{ Therefore\;A = 45° ; B = - 15°}}}}$

Step-by-step explanation:

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