If tan A -tan B = x and cot B - cot A = y, prove that `cot(A-B)=1/x+1/y`

If (tanA-tanB)=x and (cotB-cotA)=y ,then cot(A-B)

If a^x = b^y and b^x = a^y , prove that a = b

If tan^-1 x+tan^-1 y+tan^-1 z=pi , prove that x+y+z=xyz

If 2 tan beta + cot beta = tan alpha , prove that 2 tan (alpha-beta) = cot beta

If A + B + C= pi and cos A = cos B cos C, show that tan A =tan B + tan C and cot B cot C=1/2.

If cos A+cos B=1/2 and sin A +sin B=1/4 then prove that tan ((A+B)/2)=1/2 .

If tan^-1 x+tan^-1 y+tan^-1 z=pi/2 , prove that xy+yz+zx=1

In a ∆ ABC prove that tan( (A+B)/2) = cot( C/2) .

a, b, c are in G.P. If x, y are A.M.'s between a, b and b, c respectively, prove that- a/x+c/y=2 and 1/x+1/y=2/b .

If A + B + C = pi , show that cot A cot B + cot B cot C + cot C cot A = 1