Question

18.
if A, B and C are interior angles of a triangle ABC, the tan(A+B) is equal to
O A.Cotc
O B.Cot (C/2)
O C. -Tanc
O D.Tan (C/2)​

Answer 1

Step-by-step explanation:

A, B and C are the interior angles of a triangle ABC then If A, B and C are the interior angles of a triangle ABC then

A+B+C=π⟹A+B=π−C⟹A+B2=π2−C2A+B+C=π⟹A+B=π−C⟹A+B2=π2−C2

⟹tanA+B2=tan(π2−C2)⟹tan⁡A+B2=tan⁡(π2−C2)

⟹tanA+B2=sin(π2−C2)cos(π2−C2)=cosC2sinC2=cotC2