simplify expression

Question

tan^2x+secx-1/secx-1 

Answer 1

Hi Ac, tan² x = sec² x - 1 (identity.) Replacing the tan² x with sec² x - 1 gives:

sec² x -1 + sec x - 1

--------------------------

sec x - 1

Rearranging the numerator:

sec² x + sec x - 2

------------------------

sec x - 1

Factor the numerator into two binomials:

(sec x + 2) (sec x - 1)

-----------------------------

sec x - 1

The sec x - 1 cancels leaving sec x + 2.

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