Prove (sin2(x) + 4sin(x) + 3) / cos2(x) = (3 + sin(x)) / (1 - sin(x))

Here is the step by step demonstrations to prove (sin2(x) + 4sin(x) + 3) / cos2(x) = (3 + sin(x)) / (1 - sin(x)) trig identity easily.


(sin2(x) + 4sin(x) + 3) / cos2(x) = (3 + sin(x)) / (1 - sin(x)) - Trig Identities Proof

LHS
=
sin2(x) + 4sin(x) + 3

cos2(x)

=
sin2(x) + sin(x) + 3sin(x) + 3

1 - sin2(x)

=
(sin(x) + 3) × (sin(x) + 1)

(1 - sin(x)) × (1 + sin(x))

=
3 + sin(x)

1 - sin(x)

= RHS

Hence Proved.
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