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Aleah Moses
Mathematics
22 February, 15:00
1 / (Sec x Tanx) = Sec x + tan x
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Destiny Yoder
22 February, 15:26
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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.
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