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

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


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

RHS
=
cos(x)

1 - sin(x)

=
cos(x)

1 - sin(x)
×
1 + sin(x)

1 + sin(x)

=
cos(x) × (1 + sin(x))

1 - sin2(x)

=
cos(x) × (1 + sin(x))

cos2(x)

=
1 + sin(x)

cos(x)

=
1

cos(x)
+
sin(x)

cos(x)

= sec(x) + tan(x)

= LHS

Hence Proved.
Trig identities proof are made simpler and easier here. Listed here various trig identities with the step by step proof.


Related Proofs :