Question

For triangle PQR, Prove that tan [(Q+R) /2]=cotp/2 .​

Answer 1

Angle P + Angle Q + Angle R = 180°

Angle sum property of triangle (ASP)

consider above equation as 1

divide equation 1 by 2, we get

P/2 + Q/2 +R/2 = 180°

P/2 +Q/2 = 90° - R/2

taking tan to both the side,

tan (P+Q/2) = tan (90°- R/2)

tan (P+Q/2) = cot R/2

since tan (90°-0) = cot

hence proved

hope it helps you