Question

Prove that 1bycosecA-cotA+1/cosecB-cotB+1/cosecC-cotC=cosecA+cosecB+cosecC+cotA+cotB+cotC
Pro

Answer 1

Prove that

1/cosecA-cotA+ 1/cosecB-cotB +1/cosecC-cotC = cosecA + cosecB + cosecC + cotA  + cotB + cotC

Proof:

1/cosecA-cotA=1*(cosecA+cotA)/(cosecA+cotA)*(cosecA-cotA)

1/cosecA-cotA=(cosecA+cotA)/(cosec^2A-cot^2A)=cosecA+cotA

and similarly,

1/cosecB-cotB=cosecB+cotB

and again similary,

1/cosecC-cotC=cosecC+cotC

Now add all right hand side terms and we will get,

=cosecA+cotA+cosecB+cotB+cosecC+cotC

1/cosecA-cotA+ 1/cosecB-cotB +1/cosecC cotC=cosecA+cosecB+cosecC+cotA+cotB+cotC

Hence Proved!