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 $$\frac{1+\tan x}{1-\tan x}$$​​

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

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

If $$\cos^2 A + \cos^4 A = 1$$​, then the value of the expression $$\sin A + \sin^2 A$$​ is:

If $$\cos(90^\circ \theta) = \sin(\theta) \quad ( \quad 90^\circ < \theta < 90^\circ \ )$$then the value of  tan5θ is:

The value of the expression $$\left[ \cosec(75^\circ + A) - \sec(15^\circ - A) - \tan(55^\circ + A) + \cot(35^\circ - A) \right]$$​ is:

The value of $$\frac{(1+\sin A)(\tan A - \sec A + 1)\sec A}{\tan A + \sec A - (\sec^2 A - \tan^2 A)} \text{ is:}$$​