Question

if tanA/tanB=k,prove that k+1/k-1=sin(A+B)/sin(A+B)

Answer 1

You have a typo, it should be ...

if tanA/tanB=k,prove that k+1/k-1=sin(A+B)/sin(A-B)

LS = (k+1)/(k-1)
= (tanA/tanB + 1)/(tanA/tanB - 1)
= [ (tanA + tanB)/tanB ] / [tanA - tanB)/tanB ]
= (tanA + tanB)/(tanA - tanB)
= (sinA/cosA + sinB/cosB) / (sinA/cosA - sinB/cosB)
= [ (sinAcosB + sinBcosA)/(cosAcosB) ] / [ (sinAcosB - sinBcosA)/(cosAcosB) ]
= (sinAcosB + sinBcosA) / (sinAcosB - sinBcosA)
= sin(A + B) / sin(A - B)
= RS