Choice A is true. This is the Pythagorean identity. One of the most fundamental trig identities you should memorize.
Choice B is false. Let A = 60 and B = 30 and you'll see the left hand side turn into 0.5 while the right hand side turn into -0.5
Choice C is true. This is a variation of the identity tan^2+1 = sec^2 (just subtract tan^2 from both sides)
Choice D is true as this is a more complicated variation of 1+tan^2 = sec^2