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Taking L.H.S.,
cot(a+b)=1/tan(a+b)
=1-tan(a)+tan(b)/tan(a)+tan(b)
[Since,tan(a+b)=tan(a)+tan(b)/1-tan(a)tan(b)]
Dividing by tan(a)tan(b) in num and deno,we have
=cot(a)cot(b)-1/cot(a)+cot(b)
=R.H.S.
Hence Proved.
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