[ASK] Trigonometry Question

[Monox D. I-Fly]

Suppose the angles in triangle ABC is A, B, and C. If sin A + sin B = 2 sin C, the value of [tex]2tan\frac12Atan\frac12B[/tex] is ....

A. [tex]\frac83[/tex]

B. [tex]\sqrt6[/tex]

C. [tex]\frac73[/tex]

D. [tex]\frac23[/tex]

E. [tex]\frac13\sqrt3[/tex]


Since A, B, and C are the angles of triangle ABC, then C = 180° – (A + B)

sin A + sin B = 2 sin C

sin A + sin B = 2 sin(180° – (A + B))

sin A + sin B = 2 sin(A + B)

2 = [tex]\frac{sinA+sinB}{sin(A+B)}[/tex]


[tex]2tan\frac12Atan\frac12B[/tex]

[tex]\frac{sinA+sinB}{sin(A+B)}×tan\frac12Atan\frac12B[/tex]

What am I supposed to do after this?

[Guest]

D. [tex]\frac{2}{3}[/tex]

[Monox D. I-Fly]

Thank you.