Prove (cos(x) / (1 - sin(x))) - tan(x) = sec(x)

Here is the step by step demonstrations to prove (cos(x) / (1 - sin(x))) - tan(x) = sec(x) trig identity easily.


(cos(x) / (1 - sin(x))) - tan(x) = sec(x) - Trig Identities Proof

LHS
=
cos(x)

1 - sin(x)
- tan(x)

=
cos(x)

1 - sin(x)
-
sin(x)

cos(x)

=
cos2(x) - (sin(x) × (1-sin(x)))

cos(x) × (1 - sin(x))

=
cos2(x) - sin(x) + sin2(x)

cos(x) × (1 - sin(x))

=
1 - sin(x)

cos(x) × (1 - sin(x))

=
1

cos(x)

= sec(x)

= RHS

Hence Proved.
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