Question

If sin 3A = 1, then find the value of cos 2A – tan² 45°.

If (sec A + tan A) (1 – sin A) = k cos A, then find the value of k.

Rahim and Nadeem are two friends whose plots are adjacent to each other. Rahim's son made a drawing of the plots with necessary details. It is decided that Rahim will fence the triangular plot ABC and Nadeem will fence along the sides AF, FE and BE. Observe the diagram carefully and answer the following questions : (Use √2 = 1.41 and √3 = 1.73)

Evaluate (5cos²60° + 4sec²30° – tan²45°)/(sin²30° + cos²30°)

In Figure 2, the angles of elevation of the top of a tower AB of height 'h' m, from two points P and Q at a distance of x m and y m from the base of the tower respectively and in the same straight line with it, are 60° and 30°, respectively. Prove that h² = xy.