The value of $$(\sin^2 7\frac{1^{\circ}}{2}+\sin^2 82\frac{1^{\circ}}{2}+\tan^2 2^{\circ} \tan^2 88^{\circ})$$ is

$$\sin 7\frac{1^{\circ}}{2} = \sin (90^{\circ}- 82\frac{1^{\circ}}{2}) = \cos 82\frac{1^{\circ}}{2} $$
$$\sin^2 7\frac{1^{\circ}}{2} = \cos^2 82\frac{1^{\circ}}{2} $$
Similarly $$tan^2 88^{\circ} = cot^2 2^{\circ}$$
$$(\sin^2 7\frac{1}{2}^{\circ}+\sin^2 82\frac{1}{2}^{\circ}+\tan^2 2^{\circ} \tan^2 88^{\circ})$$ = $$sin^2 82\frac{1}{2}^{\circ} + cos^2 82\frac{1}{2}^{\circ} + tan^2 2^{\circ} \times cot^2 2^{\circ}$$
$$=2$$
Hence Option B is the correct answer.