Choose the correct answer:

sec²60° – 1 = ?
A. 2

B. 3

C. 4

D. 0

If θ = 45°, find the value of

(i)

(ii) cos² θ - sin² θ

Find the numerical value of the following :

sin45°.cos45° – sin²30°.

At a point A, 20 meters above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at A is 60°. Find the distance of the cloud from A.

If , where and are acute angles, find the value of .

From a point on the ground, the angle of elevation of the top of a tower is observed to be 60°. From a point 40m vertically above the first point of observation, the angle of elevation of the top of the tower is 30°. Find the height of the tower and its horizontal distance from the point of observation.

Evaluate the following :

cosec²30°.tan²45° – sec²60°

Evaluate each of the following:

Express in terms of angles between 0° and 30°.