Establish the identity. tan^2(-theta)+1=sec^2 theta

Question

Which of the following four statements establishes the​ identity?

A. tan²(-theta) + 1 = - tan²(-theta) + 1 = tan²(theta) + 1 = sec²(theta)

B. tan²(-theta) + 1 = (-tan theta)²+1 = tan²theta +1 = sec² theta

C. tan²(-theta) + 1 = (-tan theta)²+1 = tan²theta - 1 = sec²theta

D. tan²(-theta) + 1 = (sec theta)²-1 = sec²theta - 1 = sec²theta

Answer 1

B is correct. A close, C and D most wrong

the right hand sides of the last equations in C and D are wrong, so whatever went before doesn't matter.

the right hand sides of the last equations in A and B are correct, so it narrows down to A or B

tan^2(-T) = tan^2(T), so B is correct

It may help to graph tan(T) = -tan(-T),

then square both sides to get: tan^2(T) = tan^2(-T)

but this is tricky, get a sign wrong somewhere and you get the wrong answer

But for certainty, C and D are incorrect. Totally wrong. tan^2(x) +1 = sec^2(x), not what C and D have, with a sign clearly wrong.