tanx + ctgx = 2cscx
tanx = sinx/cosx, ctgx = cosx/sinx
sinx/cosx + cosx/sinx = 2csc2x
sinxsinx /sinxcosx + cosxcosx/sinxcosx = 2csc2x
sin^2(x )/sinxcosx + cos^2(x)/sinxcosx = 2csc2x
(( sin^2(x) + cps^2(x))/sinxcosx = 2csc2x
sin^2(x) + cos^2(x) = 1
1/sinxcosx = 2csc2x
2/2sinxcosx = 2csc2x
2sinxcosx = sin(2x)
2/sin(2x) = 2 csc2x
1/sinx = cscx and 1/sin(2x) = csc(2x)
2csc(2x) = 2csc(2x)