Question

If tan(A+B)= √3 , and tan(AB) = 1/√3. Find A and B if 0

Answer 1

Solution=>

Tan [A + B] = √3

Tan [A + B] = Tan 60°

[A + B] = 60°

A + B = 60 -[1]

tan[ A - B] = 1/√3

Tan [A-B] = Tan 30°

A-B = 30° -[2]

[1] - [2]

A + B = 60

A - B = 30

2 A = 90

A = 45

B = 30.

Answer 2

tan(A+B) = √3

as we know tan60° = √3

So, tan(A+B) = √3 = tan60°

So, A+B = 60° _____(i)

Also, tan(AB) = 1/√3

we know, tan30° = 1/√3

So, tan(AB) = 1/√3 = tan30°

AB = 30° ________(ii)

Now, From (i), we can write (A = 60° - B)

So, put this value of A in (ii), we get:

→ (60°-B)B = 30°

→ 60°B - B² = 30°

→ B² - 60°B + 30° = 0

Solve it...

Thankyou!!!