Prove tan2(x) + 1 + tan(x) sec(x) = (1 + sin(x)) / cos2(x)

Here is the step by step demonstrations to prove tan2(x) + 1 + tan(x) sec(x) = (1 + sin(x)) / cos2(x) trig identity easily.


Tan2(x) + 1 + tan(x) sec(x) = (1 + sin(x)) / cos2(x) - Trig Identities Proof

LHS
= tan2(x) + 1 + tan(x) sec(x)

=
sin2(x)

cos2(x)
+
cos2(x)

cos2(x)
+
sin(x)

cos(x)
×
1

cos(x)

=
sin2(x)

cos2(x)
+
cos2(x)

cos2(x)
+
sin(x)

cos2(x)

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

cos2(x)

=
1 + sin(x)

cos2(x)

= RHS

Hence Proved.
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