Question

If tan A-tan B=x; cot A-cot A =y
show that cot (A-B) = 1/x + 1/y
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Answer 1

Answer:

Cot(A-B) = cotACotB-1 / Cot + Cot B

= 1/x + 1/y

Step-by-step explanation:

Answer 2

Answer:

Given:-

• tanA-tanB=x.
• CotB-CotA=y.

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

Explanation

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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.

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

Hope it will help you.