Which of the following trigonometric identities are true?
$$\sin^{2} (41^{\circ}) + \sin^{2} (49^{\circ}) = 1$$
$$\sin^{2} (60^{\circ}) - 2\tan (45^{\circ}) - \cos^{2}(30^{\circ}) = -1$$
$$\sin^{2} (\theta) + \dfrac{1}{1 + \tan^{2} (\theta)} = 1$$

(A)
$$\sin^{2} (41^{\circ}) + \sin^{2} (49^{\circ})$$
$$\sin^{2} (41^{\circ}) + \sin^{2} ((90-41)^{\circ})$$
$$\sin^{2} (41^{\circ}) + \cos^{2} (49^{\circ})$$
$$=1$$
This is TRUE.

(B)
$$\sin^{2} (60^{\circ}) - 2\tan (45^{\circ}) - \cos^{2}(30^{\circ})$$
$$\left(\dfrac{\sqrt{3}}{2}\right)^2-2\left(1\right)-\left(\dfrac{\sqrt{3}}{2}\right)^2$$
$$=-2$$
This is FALSE

(C)
$$\sin^{2} (\theta) + \dfrac{1}{1 + \tan^{2} (\theta)} $$
$$\sin^{2} (\theta) + \dfrac{1}{\sec^{2} (\theta)}$$
$$\sin^{2} (\theta) + \cos^{2} (\theta)$$
$$=1$$
This is TRUE

Thus, statement A and statement C are TRUE.