Question

if tanA- tanB= x ,cotB - cotA = y. prove that cot(A-B)=1/x+1/y

Answer 1

First take RHS and prove for LHS.Here It is take a look at the photo

Answer 2

Given:-

• tanA-tanB=x.
• CotB-CotA=y.

Prove that, cot (A-B)=1/x+1/y.

Explanation.

LHS,

=Cot (A-B) [by formula].

=(CotA*CotB+1)/cotB-CotA.

=CotA*CotB/CotB-CotA+1/cotB-CotA.

=1/tanA*1/tanB/1/tanB-1/tanA+1/CotB-CotA.

=1/tanA*tanB/(tanA-tanB)/tanA*tanB+1/CotB-CotA.

1/tanA*tanB will be cancelled out.

so,

=1/(tanA-tanB)+1/(Cot B-Cot A).

=1/x+1/y.

=RHS.

Formula used.

• CotA=1/tanA.
• Cot(A-B)=CotA CotB+1/CotB-CotA.

Step-by-step explanation:

Hope it will help you.