Question

Which expression is equivalent to sec^2x − 1? a. cot2x b. tan2x c. csc2x d. cos2x

Answer 1

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 2

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.