Question 596068
verify the identity algebraically, 

cos x/sin x +1 minus cos x/sin x-1 =2sec x
these problems just make no sense at all
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And those problems about people's ages do?
Don't people know how old they are?
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The idea is to prove that the statement is true, or to disprove it.
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I think you mean:
cos x/(sin x +1) - cos x/(sin x-1) =2sec x
Get rid of fractions
cos*(sin - 1) - cos*(sin + 1) = 2sec
cos*sin - cos - cos*sin - cos = 2sec
-2cos = 2sec
That's not true, not an identity.