If A + B = `(pi)/(4)`, show that
(cot A - 1) (cot B - 1) = 2 and hence deduce that cot `22^((1^(0))/(2))=sqrt(2)+1.`

Suppose that A+B =135^(@) and neither A nor B is an intergral multiple of 180^(@) . Then prove that (1 + cot A)(1 + cot B) = 2 and hence deduce that cot67(1^(@))/(2) = sqrt(2)- 1 .

Show that (cot A + tan B) / (cot B + tan A) = cot A. tan B.

If A+B+C= pi//2 then show that cot A + cot B+ cot C=cot A cot B cot C

If A+B=135^(@) " then " (1+ cot A ) (1+cot B)=

Show that (1- tan ^(2) A ) /( cot ^(2) A-1) =tan ^(2) A

Show that cot(A+15^(@))-tan(A-15^(@))=(4cos2A)/(1+2sin2A) deduce that cot15^(@)=2+sqrt(3)

The value of cot^(-1)(2+sqrt(3)) is

Show that (cot A - cos A)/(cot A + cos A) = ( cosec A - 1)/(1 + cosec A)

If 2A is not an integral multiple of pi , then show that i) cot A+tan A=2"cosec " 2A ii) cot A-tan A=2 cot2A and deduce the values of tan52 1^(@)/2 and tan37 1^(@)/2