Question

how to prove this trigonometric identity
sec x- tan x= 1-sin x/cos x

Answer 1

i know that sec x equals to 1/cos x so that equation would be
1/cos x -tan x=1-sin x/cos x

Answer 2

Hints:
sec x = 1/cos x
tan x = sinx / cosx

Answer 3

i know that info, but do i subtract the 1/cos x to the other side

Answer 4

You don't start with an equality to prove an equality

Answer 5

sec x - tan x
= 1/cosx - sinx/cosx
= (1-sinx)/cosx

Answer 6

You can't do this:
secx - tanx = (1-sinx)/cosx
1/cosx - tanx = 1/cosx - sinx/cosx
1/cosx - tanx = 1/cosx - tanx

Answer 7

This is one of the common mistakes that people make when proving anything

Answer 8

why would the equation become sec x - tan x
= 1/cosx - sinx/cosx
= (1-sinx)/cosx

Answer 9

tan x = a/b = (a/c)/(b/c) = sinx/cosx

Answer 10

tanx=sinx/cosx will be used often in trigonometry, you'd better memorize it

Answer 11

after the equation becomes into this sec x - tan x
= 1/cosx - sinx/cosx
= (1-sinx)/cosx
what will we have to do next

Answer 12

Or more completely:
LHS
=secx - tanx
=1/cosx - sinx/cosx
=(1-sinx)/cosx
=RHS

Answer 13

sec -tan x =(1-sinx)/cos x
i see it know thank you very much

Answer 14

no problem