If tanA+tanB=a and cotA+cotB=b, then prove that cot(A+B)=1/a-1/b

Steps to prove cot(A+B)=1/a-1/b

R.H.S

=1/a-1/b

=1/(tanA+tanB)-1/(cotA+cotB)

=1/(1/cotA+1/cotB)-1/(cotA+cotB)

=cotA.cotB/(cotB+cotA)-1/(cotA+cotB)

=(cotA.cotB-1)/(cotB+cotA)

=cot(A+B)

L.H.S

Hence cot(A+B)=1/a-1/b is proved.

Detail Information:-

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