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Prove that: (tan(A+B))/(cot(A-B))=\ (tan...

Prove that: `(tan(A+B))/(cot(A-B))=\ (tan^2A-tan^2B)/(1-tan^2Atan^2B)`

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Given,`(tan(A+B))/(cot(A-B))`
`=((tanA+tanB​​)/(1−tanA.tanB))/cot(A-B)`
as `cot(A-B)=1/tan(A-B)`
`=((tanA+tanB​​)/(1−tanA.tanB))/(1/tan(A-B))`
`=((tanA+tanB​​)/(1−tanA.tanB))/(1/((tanA+tanB​​)/(1−tanA.tanB)))`
`=((tanA+tanB)/(1−tanA.tanB)​​)/((1+tanA.tanB​)/(tanA−tanB))`
...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
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  2. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

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  5. If tan(A+B)=x and tan(A-B)=y then find the values of tan2A and tan2B

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