Verified Answer :

Sec^2 x - 1 = tan^2x

Proof:
Sec^2x = 1+ tan^2x

1/cos^2x = 1 + sin^2x/cos^2x

1/cos^2x - sin^2x/cos^2x = 1
Using common denominator:
(1-sin^2x)/cos^2x = 1
sin^2x + cos^2 x = 1
cos^2 x = 1 - sin^2x
Substituting : 
cos^2x/cos^2x = 1
1 = 1
Left hand side = right hand side

Answer:

option B tan²x

Step-by-step explanation:

We have to simplify the expression given as ( \(sec^{2}\)x-1 )

Since sec x = \(\frac{1}{cosx}\)

so ( \(\frac{1}{cosx}\) )² - 1 = \(\frac{1}{cos^{2} x}\) - 1

=\(\frac{1-cos^{2}x }{cos^{2}x}\)

= \(\frac{sin^{2}x }{cos^{2}x}\)

= tan²x

Therefore, option B tan²x is the answer.

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