If tan A = a/(a+1) and tan B = 1/(2a+1) , then find the value of A + B.

Question

If tan A = \(\frac{a}{a+1}\) and tan B = \(\frac{1}{2a+1}\), then find the value of A + B.

Answer 1

We know that,

tan (A + B) = \(\frac{tan\,A+tan\,B}{1-tan\,A\,tan\,B}\)

∴ tan(A + B) = \(\frac{\frac{a}{a+1}+\frac{1}{2a+1}}{1-(\frac{a}{a+1})(\frac{1}{2a+1})}\)

⇒ tan(A + B) = \(\frac{a(2a+1)+(a+1)}{(a+1)(2a+1)-a}\)

⇒ tan(A + B) = \(\frac{2a^2+2a+1}{2a^2+2a+1}\)

⇒ tan(A + B) = 1

⇒ tan(A + B) = tan \((\frac{x}{4})\)

⇒ A + B = \(\frac{x}{4}\)