Evaluate:

A ladder makes an angle of 60° with the ground and its bottom is 3.7 m away from the wall. Find its length.

Simplify: cosecθ(1 – cosθ)(cosecθ + cotθ)

If cot ⁡A + cos ⁡A = p, cot ⁡A - cos ⁡A = q, then what is the value of p²- q²?​​

What is the value of sin 20° cos 10° + cos 20° sin 10°?

If sin x = $$\frac 35$$​ and x ∈ (0, $$\frac{\pi}2$$​), then find $$\frac{1+\tan x}{1-\tan x}$$​​

Aditya is standing on a light house of 150 m height and watching two boats on either side with angles of depression of 30^o and 60^o, respectively. Find the distance between the two boats.

A flagstaff stands on the top of a building. At a distance of 30 m away from the foot of the building, the angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 30°. Find the height (in metres) of the flagstaff.

​Find the value of $$\frac{1 - \sec^2 \theta}{\sin^2 \theta} \times \cos^2 \theta$$​​​

The angles of elevation of the top of a tower from two points X and Y (on opposite sides of the tower) at distances b² m and a² m, respectively, from the base and in the same straight line with it are complementary. The height (in m) of the tower is ________.

If sin θ + cos θ = √3, then the value of tan θ + cot θ is: