Prove that the distance between the points `(a + r costheta, b + r sintheta)` and `(a, b)` is independent of `theta`.

The distance between the points (costheta,sintheta) and (sintheta,-costheta) is

Write the distance between the points A(10costheta,\ 0) and B(0,\ 10sintheta) .

What is the distance between the points A(sintheta-costheta,\ 0) and B(0,sintheta+costheta) ?

Find the maximum distance between the points (3sintheta, 0, 0) and (4costheta, 0, 0).

Prove that the determinant [(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x)] is independent of theta .

Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]| is independent of theta

Write the value of theta in (0,\ pi/2) for which area of the triangle formed by points O(0,0),\ A(a\ costheta,\ b sintheta)a n d\ B(a\ costheta,\ -b\ sintheta) is maximum.

If the angle between the vectors a and b be theta and a*b=costheta then the true statement is

Find the least and greatest values of the distance of the point (costheta,sintheta),theta in R , from the line 3x-4y+10=0.

Find the least and greatest values of the distance of the point (costheta,sintheta),theta in R , from the line 3x-4y+10=0.