Prove tan(x) sin(x) + cos(x) = sec(x)

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


Tan(x) sin(x) + cos(x) = sec(x) - Trig Identities Proof

LHS
= tan(x) sin(x) + cos(x)

=
sin(x)

cos(x)
× sin(x) + cos(x)

=
sin2(x)

cos(x)
+ cos(x)

=
sin2(x) + cos2(x)

cos(x)

=
1

cos(x)

= 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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