Question

if sin x + cos x =sqrt 3, prove that tan x + cot x = 1

Answer 1

sinx+cosx=3^(1/2)
tanx+cotx=sinx/cosx + cosx/sinx = (sinx)^2 + (cosx)^2 / sinxcosx= 1/sinxcosx
now, squaring  the first equation, we have,
sinx^2+cosx^2+2sinxcosx=3
1+2sinxcosx=3
so, sinxcosx=1
putting it in the second equation,
tanxcotx= 1/sinxcosx=1
hence proved.