Question

if tan A+B =√3 and tan A -B = 1/√3. 0° is smaller than A+B and A+B is smaller than or equals to 90 ° , find the value of A and B when A is bigger then B​

Answer 1

Answer:

A+B = 60° as tan 60 = √3

A-B = 30° as tan 30 = 1/√3

on solving for both A=45°

and B = 15°

Answer 2

Answer:

A = 45°

B = 15°

Step-by-step explanation:

Given:-

• tan A+B = √3
• tan A -B = $\frac{1}{ \sqrt{3} }$
• 0° is smaller than A+B
• A+B is smaller than or equal to 90°

We are supposed to find the value of A and B

• when A is bigger then B.

Let's proceed!!

tan A+B = √3

Also,

tan 60° = √3

$\implies$ A + B = 60° _____(1)

And,

tan A - B = $\frac{1}{ \sqrt{3} }$

Also,

tan 30° = $\frac{1}{ \sqrt{3} }$

$\implies$ A - B = 30° _______(2)

From (1)

A = 60° - B

Putting value of A in (2) we get,

60° - B - B = 30°

-2B = 30° - 60°

-2B = -30°

B = $\large\frac{\cancel{-30°}}{\cancel{-2}}$

$\boxed{B = 15°}$

$\therefore$ A = 60° - 15° {from (2)}

$\boxed{A = 45°}$