Question

If tan(A+B)= Cot(A-B)= √​3​​; 0°<A+B
⩽90°; A>B; find A and B

Answer 1

value of A is 45 and B is 15

Answer 2

Given,

tan(a+b)=√3

cot(a-b)=√3

To Find,

The value of a and b =?

Solution,

We know that value of tan 60° is √3  and cot 30° is √3 from the trigonometric table. Therefore,

tan(a+b) = √3  = tan 60°

tan 60° = tan(a+b)

cot(a-b)=√3 = cot 30°

cot 30° = cot(a-b)

Equating angles on both sides,

a + b = 60° ⇒ Equation 1

a -  b = 30° ⇒ Equation 2

Adding equation 1 and 2

a + b + a - b = 60° + 30°

2a  = 90°

a = 90 / 2

a = 45°

Putting the value of a in equation 1, we get

45 + b = 60°

b = 60° - 45°

b = 15°

Hence, If tan(A+B)= Cot(A-B)= √​3​​; 0°<A+B⩽90°; A>B then the values of a and b are 45° and 15° respectively.