Question

tan (A+B/2)=cot C/2​

Answer 1

Answer:

(2∠A+∠C)=cot(2B)

Step-by-step explanation:

\begin{gathered}We \: know \: that,\\ In \: Triangle \: ABC , \\\angle A + \angle B + \angle C=180\degree\end{gathered}Weknowthat,InTriangleABC,∠A+∠B+∠C=180°

( Angle sum property )

\implies \angle A+\angle C = 180\degree - \angle B⟹∠A+∠C=180°−∠B

Divide both sides by 2 , we get

\implies \frac{\angle A+ \angle C}{2}=\frac{180}{2}-\frac{B}{2}⟹2∠A+∠C=2180−2B

\implies \frac{\angle A+ \angle C}{2}=90\degree -\frac{B}{2}⟹2∠A+∠C=90°−2B

\implies tan\big(\frac{\angle A+ \angle C}{2}\big)=tan\big(90\degree -\frac{B}{2}\big)⟹tan(2∠A+∠C)=tan(90°−2B)

\implies tan\big(\frac{\angle A+ \angle C}{2}\big)= cot(\frac{B}{2})⟹tan(2∠A+∠C)=cot(2B)

/* Since ,

tan(90° - A) =cotA */