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Based on the question, here is the diagram.

Let the angle made by the ladder with respect to the ground = θ

The trigonometric function, cos(θ) = (adjacent side)/ (hypotenuse)

Therefore, cos(θ) = 4m/5m

This gives: cos(θ) = 4/5-> θ = cos

This implies: θ = 36.87°

Therefore the angle made by the ladder with the ground = 36.87°.

Here let’s start with the left-hand side of the equation -> tan(x) + cot(x)

We can also write the above expression as: tan(x) + cot(x) = [sin(x/cos(x)] + [cos(x)/sin(x)]

Here we can take a common denominator and this gives: [sin

According to the trigonometric identity, sin

Hence we get: 1/ [(sin(x) * cos(x)] = right-hand side of the equation!

Henceproved!