Question

if cos tita=cas A-cos B/1-cos Acos B prove tan tita/2=-tan A /2tan B/2

Answer 1

HI, cosθ=cosA−cosB1−cosAcosB1−tan2θ21+tan2θ2=cosA−cosB1−cosAcosBUsing componendo−divindo rule, 1−tan2θ2+1+tan2θ21−tan2θ2−1−tan2θ2=cosA−cosB+1−cosAcosBcosA−cosB−1+cosAcosB−1tan2θ2=cosA+1−cosB−cosAcosBcosA−1−cosB+cosAcosB−1tan2θ2=(cosA+1)−cosB(1+cosA)(cosA−1)+cosB(cosA−1)−1tan2θ2=(cosA+1)(1−cosB)(cosA−1)(1+cosB)=(2cos2A2−1+1)(1−1+2sin2B2)(1−2sin2A2−1)(1+2cos2B2−1)−1tan2θ2=cos2A2sin2B2sin2A2cos2B2=tan2B2tan2A2tan2θ2=−tan2A2tan2B2=−tan2A2cot2B2tanθ2=−tan2A2cot2B2