tan x in terms of sec x?

Answer 1

start with Pythagorean identity...

[ i'll leave out the x, for now ... ]

sin^2 + cos^2 = 1

divide by cos^2

tan^2 + 1 = sec^2 .... why?

( sin^2) / ( cos^2) = tan^2, and 1 / ( cos^2) = sec^2

thus .... sec( x) = + - sqrt ( 1 + tan^2 ( x ) )

or .... tan ( x) = + - sqrt ( sec^2 ( x) - 1 )

Answer 2

Start with the identity

[sinx]^2 + [cosx]^2 =1

divide both sides by [cosx]^2, and you get

[tanx]^2 +1 = [secx]^2

so

tanx = (+ or - ) sqrt( [secx]^2-1)

Answer 3

tan =sin/cos
tan^2=sin^2/cos^2
=(1-cos^2)/cos^2
=1/cos^2- 1
=sec^2-1
Hence tan=sqrt(sec^2-1)

Answer 4

tanx=sinx/cosx
secx=1/cosx
tanx=sinx*1/cosx
tanx=sinxsecx