If cos x−sinαcotβsin x=cosα ,
then the value of tan(x2) is
The given equation can be written as
1−tan2(x2)1+tan2(x2)−sinα cotβ2tan(x2)1+tan2(x2)=cosα⇒tan2x2(1+cosα)+sinα cotβ.2tanx2−(1−cosα)=0⇒tan2x2+2sinαcotβ1+cosαtanx2−1−cosα1+cosα=0⇒tan2x2+2tanα2cotβtanx2−tan2α2=0⇒tan2x2+2tanα2.12(cotβ2−tanβ2)tanx2−tan2α2=0⇒(tanx2+cotβ2tanα2)(tanx2−tanβ2tanα2)=0⇒tan(x2)=−tan(α2)cot(β2) or tan(x2)=tan(α2)tan(β2)