Use basic identities to simplify the expression. sin2θ + tan2θ + cos2θ

I think the correct expression for the problem would be as follows:

sin^2 (θ) + tan^2 (θ) + cos^2 (θ)

To be able to simplify this, we need to have knowledge on the different trigonometric identities. These identities are expressions which would relate the different trigonometric functions. For this case, we use two known basic identities. These are

sin^2 (θ) + cos^2 (θ) = 1 
1 + tan^2 (θ) = sec^2 (θ)

We simplify as follows:
sin^2 (θ) + tan^2 (θ) + cos^2 (θ) = sin^2(θ) + tan^2 (θ) + cos^2 (θ)
                                                 = 1 + tan^2 (θ)
                                                 = sec^2 

Therefore, the expression sin^2 (θ) + tan^2 (θ) + cos^2 (θ) is equal to sec^2 (θ). Other form that would also be equivalent to the same expression would be sin^2 (θ) + sin^2 (θ) / cos^2 (θ) + cos^2 (θ).