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

Prove that `:(tan(A+B))/("cot"(A-B))=(sin^2A-sin^2B)/(cos^2A-sin^2B)`

Text Solution

Verified by Experts

Given,L.H.S=`(tan(A+B))/("cot"(A-B))`
=`(tan(A+B))(tan(A-B))`
=`((sin(A+B))/(cos(A+B)))((sin(A-B))/(cos(A-B)))`...(1)
As `sin(A+B)xx sin(A-B)=sin^2A-sin^2B`
`cos(A+B)xx cos(A-B)=cos^2A-cos^2B`
Thus,equation (1) becomes
`(sin^2A-sin^2B)/(cos^2A-sin^2B)`=R.H.S
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