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

Prove that the distance between the points (a+r cos theta,b+r sin theta) and (a,b) is independent of theta

The distance between the points (a cos theta+b sin theta,0) and (0,a sin theta-b cos theta)

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 determinate abs([x,sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]) is independent of theta

Prove that- costheta.tantheta=sintheta

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

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

Find the relation obtained by eliminating theta " from the equations " x = r cos theta + s sintheta and y=r sintheta-s cos theta .

If r=1-costheta," then "r(d theta)/(dr)=