If θ lies in the first quadrant and cos²θ - sin²θ = $$\frac{1}{2}$$, then the value of tan²2θ + sin²3θ is:

A. $$\frac{4}{3}$$

B. 3

C. $$\frac{7}{2}$$

D. 4

Answer: Option D

Solution(By Examveda Team)

cos²θ - sin²θ = $$\frac{1}{2}$$
cos2θ = $$\frac{1}{2}$$
cos2θ = cos60°
2θ = 60°
θ = 30
tan²2θ + sin²3θ
= tan²60° + sin²90°
= 3 + 1
= 4