Question

In a ΔABC, 

(i) sin (A/2) sin (B/2) sin(C/2) > 0 

(ii) sin A sin B sin C > 0 then .....

(a) Both (i) and (ii) are true 

(b) Only (i) is true 

(c) Only (ii) is true 

(d) Neither (i) nor (ii) is true

Answer 1

(a) Both (i) and (ii) are true

When A + B + C = 180°

When A + B + C = 180° each angle will be lesser than 180° 

So sin A, sin B, sin C > 0 

⇒ sin A sin B sin C > 0 

So both (i) and (ii) are true