How do you simplify tanx - sec^2x / tanx ?

Question

**using trigonometric identities

Answer 1

Simplify tanx - sec²x / tanx.

tanx - sec²x / tanx = tanx - (1/cos²x) / (sinx/cosx)

= sinx/cosx - (1/cosx) / sinx

= sin²x/(cosx*sinx) - 1/(cosx*sinx) = (sin²x - 1)/(cosx*sinx)

= -cos²x / (cosx*sinx) = -cosx / sinx = -cotx

Answer 2

First u got to get rid of sec^2x

to do this u must know cos^2x+sin^2x=1
then divide that by cos^2x and u get 1+tan^2x=sec^2x

replace sec^2x with 1+tan^2x
so u have
tanx - 1+tan^2x
tanx
now do tanx times (tanx/tanx) so u get (tan^2x / tanx)

so now u have (tan^2x / tanx)- ( (1/tanx)+(tan^2x / tanx) )

(tan^2x / tanx)-(tan^2x / tanx)=0
so the anwser is -1/tanx which becomes -cotx

Answer 3

Is the problem tanx - (sec^2x / tanx) or (tanx - sec^2x) / tanx ?
Either way, sec^2x = tan^2x + 1

In the first case,
tanx - ((tan^2x +1) / tanx) = tanx - tanx - cotx = -cot(x)

In the second case,
(tanx - (tan^2x + 1)) / tanx = 1 - tan(x) - cot(x)

Answer 4

well sec^2(x)=(1/cosx)2
tanx=sinx/cosx

so...
(sinx/cosx - (1/cosx)^2)/(sinx/cosx)

now try it...