Evaluate

D) sin 15° sec 75°

By trigonometric identities, we can say

sin (90° - θ) = cos θ

And sec θ = 1/cos θ

Replace θ by 75°.

We get

sin (90° - 75°) = cos 75°

⇒ sin 15° = cos 75° [∵, 90° - 75° = 15°]

And sec 75° = 1/cos 75°

Using these values, we can solve the given expression.

sin 15° sec 75° = sin 15°/cos 75°

⇒ sin 15° sec 75° = cos 75°/cos 75°

⇒ sin 15° sec 75° = 1