Question

In ΔABC , if tan ,tan ,tan 222

ABC are in H.P., then a,b,c are in​

Answer 1

Answer:

→tanA/2,tanB/2,tanC/2 are in HP

⇒tanA/21,tanB/21,tanC/21 are in A.P

⇒tanB/22=tanA/21+tanC/21

⇒2cotB/2=cotA/2+cotC/2

⇒2cot(2π−(A+C))=cotA/2+cotC/2

⇒2tan(2A+C)=cotA/2+cotC/2

⇒2[1−tanA/2tanC/2tanA/2+tanC/2]=tanA/2tanC/2tanA/2+tanC/2

let tanA/2tanC/2=y

⇒1−y2=y1⇒2y=1