Question

What is a simplified form of the expression sec^2x-1/sin x sec x ?
a)cot x
b)csc x
c)tan x
d)sec x tan x
Please help me :(

Answer 1

One of the basic trig identities is : tan^2 x = sec^2 x - 1
so...
(sec^2x-1)/(sin x sec x) , notice I fixed your typing
= tan^2 x /(sinx secx)
= (sin^2 x/cos^2 x)*(1/sinx)(cosx)
= sinx / cosx
= tanx

Answer 2

If your expression mean:

( sec² x - 1 ) / ( sin x ∙ sec x ) then:


sec² x = 1 / cos² x


sec² x - 1 = 1 / cos² x - 1 = 1 / cos² x - cos² x / cos² x =

( 1 - cos² x ) / cos² x = sin² x / cos² x = tan² x


sin x ∙ sec x = sin x ∙ 1 / cos x = sin x / cos x = tan x


( sec² x - 1 ) / ( sin x ∙ sec x ) = tan² x / tan x = tan x