I will assume you meant
(tan^2 Ø + 1)/sec Ø = sec Ø
by the Pythagorean identity
tan^2Ø + 1 = sec^2 Ø , so ....
LS = sec^2 Ø/secØ
= secØ
= RS
Verify that each trigonometric equation is an identity tan^2+1/sec α =sec α
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