Solve the following for tan^2 theta.

Question

1 + tan^2 theta = secant^2 theta.

A. Tan² theta = secant² theta + 1.

B. Tan² theta = secant² theta - 1.

C. Tan theta = secant theta - 1.

D. tan² theta = opposite/adjacent.

Answer 1

B. tan^2(theta) = sec^2(theta) - 1 is correct

A has the wrong sign for 1

C has a false square root of (sec^2(theta) -1), it's not the square root of sec^2(theta) - square root of 1

D would be true if it had said tan^(theta) = (opposite side)^2/(adjacent side)^2 = hypotenuse^2/adjacent side^2