Question

In AABC, prove that tan (A + B)/2 = cot C/2​

Answer 1

Answer:

In any traingle ABC,∠A+∠B+∠C=180

∘

⇒∠A+∠B=180∘ −∠C

⇒∠A+∠B÷2= 180° −∠C÷2

⇒ 2÷∠A+∠B=90∘ − 2÷∠C

⇒tan( 2÷∠A+∠B )=tan(90 ∘− 2÷∠C)

∴tan( 2

÷∠A+∠B )=cot 2÷∠C