Question

if tan(A+B)=√3 , tan(A-B)=0 find the valve of sin(A-B)​

Answer 1

Answer:

45 and 15

Step-by-step explanation:

tan (A + B) = √3

Since √3 = tan60°

Now substitute the degree value

⇒tan (A + B) = tan 60°

(A + B) = 60° ... (i)

tan (A– B) = 1/√3

Since 1/√3 = tan30°

Now substitute the degree value

⇒tan (A - B) = tan 30°

(A - B) = 30° ... equation (ii)

Now add the equation (i) and (ii), we get A + B + A - B = 60° + 30°

Cancel the terms B

2A = 90°

A= 45°

Now, substitute the value of A in equation (i) to find the value of B 45° + B = 60°

B = 60° - 45°

B = 15°

Therefore

A = 45° and B = 15°