Evaluate the following.

D. 2tan² 45° + cos² 30° - sin² 60°

By trigonometric identities,

sin 60° = √3/2

tan 45° = 1

cos 30° = √3/2

Putting these values in 2 tan² 45° + cos² 30° - sin² 60°, we get

2 tan² 45° + cos² 30° - sin² 60° = 2(1)² + (√3/2)² – (√3/2)²

⇒ 2 tan² 45° + cos² 30° - sin² 60° = 2

Thus, 2 tan² 45° + cos² 30° - sin² 60° = 2.