Answer:
Step-by-step explanation:
to prove that 1/ (sec x - tan x) = sec x + tan x
from the right hand side sec x + tan x =
from trigonometry basics
sec x = 1/ cos x
tan x = sin x/ cos x
so, sec x + tan x = 1/ cosx + sinx/ cosx
finding the lcm
= (1+ sinx)/cos x
= (1 + sinx) cosx/ cos²x
= (1 + sinx) cosx/( 1- sinx) ( 1 + sinx)
( 1 + sinx) cancels the (1- sinx) at the denominator
so we have;
= cos x/ 1 -sinx
1/1/cosx - sinx/cosx
remember that 1/ cos x = sec x
and also sinx/cos x = tan x
so therefore we have 1/ sec x - tanx
since LHS = RHS then we can say that 1 / sec x - tan x = sec x + tan x.
