What is the value of $\sin\left(2\text{n}\pi+\frac{5\pi}{6}\right)\sin\left(2\text{n}\pi−\frac{5\pi}{6}\right)$ where n ∈ Z ?

If 1 + 2(sin x + cos x)(sin x − cos x) = 0 where 0 < x < 360°, then how many values does x take ?

Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with the positive direction of x-axis :

1. The line passes through the point $\left(1, \frac{1}{2−\sqrt{3}}\right)$.

2. The line entirely lies in first and third quadrants.

Which of the statements given above is/are correct ?

If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?