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

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