show that cot^2x + cos^2x = cos^2x -cot^2x,

Question

pre calculus

Answer 1

cot^2x + cos^2x = cos^2x - cot^2x

if it means (cotx)^2 + (cosx)^2 = (cosx)^2 - (cotx)^2

then cancel the (cosx)^2 from both sides leaving

(cotx)^2 = -(cotx)^2

take square roots of both sides

cotx = icotx

divide by cotx

1 = i which is impossible, No real solution possible

so maybe you really meant cot^(2x) + cos^(2x) = cos^(2x) - cot^(2x) then

cancel the cos^(2x) leaving cot^(2x) = - cot^(2x)

divide by cot^(2x) leaving 1 = -1 which is also impossible. No real solution possible