If A, B, and C are the angles of ΔABC, show that cot(B+C2) = tan(A2).
Answer:
- We know that the sum of the angles of a triangle is 180∘. ∴ A+B+C=180∘⟹B+C2=90∘−A2⟹cot(B+C2)=cot(90∘−A2)⟹cot(B+C2)=tanA2[ ∵cot(90∘−θ)=tanθ ]
- Thus, cot(B+C2)=tanA2.