Prove cos(x) / (1 + sin(x)) + (1 + sin(x)) / cos(x) = 2 sec(x)

Here is the step by step demonstrations to prove cos(x) / (1 + sin(x)) + (1 + sin(x)) / cos(x) = 2 sec(x) trig identity easily.


Cos(x) / (1 + sin(x)) + (1 + sin(x)) / cos(x) = 2 sec(x) - Trig Identities Proof

LHS
=
cos(x)

1 + sin(x)
+
1 + sin(x)

cos(x)

=
cos2(x) + (1 + sin(x))2

cos(x) × (1 + sin(x))

=
cos2(x) + 12 + sin2(x) + 2 sin(x)

cos(x) × (1 + sin(x))

=
(cos2(x) + sin2(x)) + 12 + 2 sin(x)

cos(x) × (1 + sin(x))

=
1 + 1 + 2 sin(x)

cos(x) × (1 + sin(x))

=
2 + 2 sin(x)

cos(x) × (1 + sin(x))

=
2 (1 + sin(x))

cos(x) × (1 + sin(x))

=
2

cos(x)

= 2 ×
1

cos(x)

= 2 sec(x)

= RHS

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


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