Prove 1 - 2cos2(x) = (tan2(x) - 1) / (tan2(x) + 1)

Here is the step by step demonstrations to prove 1 - 2cos2(x) = (tan2(x) - 1) / (tan2(x) + 1) trig identity easily.

1 - 2cos2(x) = (tan2(x) - 1) / (tan2(x) + 1) - Trig Identities Proof

RHS
=
tan2(x) - 1

tan2(x) + 1

=
sin2(x)

cos2(x)
- 1

sin2(x)

cos2(x)
+ 1

=
sin2(x) - cos2(x)

cos2(x)

sin2(x) + cos2(x)

cos2(x)

=
sin2(x) - cos2(x)

cos2(x)
× cos2(x)

= sin2(x) - cos2(x)

= 1 - cos2(x) - cos2(x)

= 1 - 2cos2(x)

= LHS

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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