Question

If tan (A + B) - V3 and tan (A - B) = 1, 0°
<A + B < 90°; A > B, then find A and B.
​

Answer 1

tan a+b =✓3

a+b = 60

tan a-b= 1/✓3 a-b = 30

so we have 2A =90 =45

from eq 1 we have a+b=60

B = 60-45 = 15

B=15

Answer 2

Step-by-step explanation:

Given:-

tan (A + B) = V3 and tan (A - B) = 1,

0°<A + B < 90°; A > B

To find:-

If tan (A + B) = V3 and tan (A - B) = 1,

0°<A + B < 90°; A > B, then find A and B.

Solution:-

Given that :-

Tan (A + B) = √3

=>Tan (A + B) = Tan 60°

A + B = 60° ---------(1)

Tan (A - B)= 1

=>Tan(A - B) = Tan 45°

A - B = 45° ---------(2)

On solving (1)&(2)

A + B = 60°

A - B = 45°

(+)

___________

2 A + 0= 105°

___________

=>2 A = 105°

=> A = 105°/2

A= 52.5°

On Substituting the value of A in (1) then

=>52.5° + B = 60°

=>B = 60° - 52.5°

=> B = 7.5°

Answer:-

The value of A = 52.5°

The value of B = 7.5° for the given problem

Check:-

If A = 52.5° and B = 7.5° then

1)LHS=Tan (A+ B)

=>Tan (53.5°+7.5°)

=>Tan60°

=>√3= RHS

LHS=RHS

2)Tan(A-B)

=>Tan(52.5°-7.5°)

=>Tan45°

=>1=RHS

LHS=RHS

Used formulae:-

• Tan 60°=√3
• Tan 45°=1