simplify: (sinxcosx-tanx)/(tan(-x)sin^2x)?

Answer 1

(sinx cosx - tanx) / (tan(-x) (sinx)^2)
= [ (sinx/cosx) (cosx)^2 - tanx] / [-tanx (sinx)^2]
= [tanx (cosx)^2 - tanx] / [-tanx (sinx)^2]
= [-(cosx)^2 + 1] / (sinx)^2
= [1 - (cosx)^2] / (sinx)^2
= (sinx)^2 / (sinx)^2
= 1

Answer 2

1

Answer 3

I'll try to make tis as clear as possible:
(sinXcosX - tanX)/-tanXsin^2X bcoz tan (-x) = -tan x
sinXcosX-tanX/ (-sinX/cosX)sin^2X becoz -tan X = (-sinX/cox X)
sinXcox-tanX/ (-sin^3X/cosx)
sinXcosX - tanX * (-cosX/sin^3X)
sinXcos^2X - sinX / (-sin^3X)
sinX(cos^2X -1) / (-sin3x) becoz sinX is common factor
(cos^2X-1)/(-sin^2X) simplification of sinX
(1-cos^2X)/sin^2X multiplication by -1
sin^2X/sin^2X sin^2X + cos^2X= 1 <=> sin^2X = 1- cos^2X
=1

Answer 4

REPORTED!