Simplify the expression

Question

1/cot^2(x) +tan(x)tan(pi/2 -x)

Answer 1

tan(π/2 - x) = sin(π/2 - x) / cos(π/2 - x)

= [sin(π/2)cosx - cos(π/2)sinx] / [cos(π/2)cosx + sin(π/2)sinx] = cosx / sinx = cotx

So, 1 / cot²x - tanx tan(π/2 - x) = tan²x - tanx(cotx) = tan²x - 1

Answer 2

1/cot²x = tan²x

tan x tan(90°-x)= tan² = tan x (-tan x) = - tan² x

therefore the sum is 0