ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
1/2
In ∆ABC,∠A + ∠B + ∠C =180° => ∠A + ∠B=180°- ∠C Dividing both sides by '2', =>(A+B)/2=90°-C/2 ----------(i) Given: sin (A+B))/2= √3/2 Substituting value from equation (i), we get: => sin (90°-θ)=cos θ Using, => cos C/2=√3/2 =>C/2=cos-1 √3/2 =>C/2=30° =>∠C=30 ×2=60° = sin (30°)=1/2
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