If $\cos(\theta-\alpha)=a$ and $\sin(\theta-\beta)=b$, then the value of $\cos^2(\alpha-\beta)+2ab\sin(\alpha-\beta)+\cos^2(\theta-\alpha)$ is...

The general solution of $\cos\theta - \sin\theta = 1$ is

The equation of the straight line passing through the point $(-5, 3)$ such that the portion of the line intercepted between the axes is divided by the point in the ratio $4:3$ (from the X-axis to the Y-axis) is...

If the equation $kx^2 - 5xy + 6y^2 + x - 3y = 0$ represents a pair of straight lines, then the co-ordinates of their point of intersection are