Eliminate `theta and phi` between `x = r cos thetaw cos phi, y = r cos theta sin phi, z = r sin theta`

Eliminate theta between the equation : x= h+a cos theta, y=k+ b sin theta .

If sin theta+ sin phi= a and cos theta+ cos phi= b , find : cos (theta+ phi) .

If sin theta+ sin phi= a and cos theta+ cos phi= b , find : cos (theta- phi) .

Eliminate theta between the equation : x = sin theta + cos theta, y = sin theta-cos theta .

Find dy/dx when x = cos theta + cos 2 theta, y = sin theta + sin 2 theta)

If sin theta+ sin phi= a and cos theta+ cos phi= b , find : sin (theta+ phi) .

Show that the equations of the normal at any point theta on the curve x = 3 cos theta - cos^3 theta, y = 3 sin theta - sin ^3 theta is 4(y cos^3 theta - x sin^3 theta) = 3 sin 4 theta

If x=r sin theta cos phi, y= r sin theta sin phi, z=r cos theta , prove that x^2+y^2+z^2=r^2 .

Eliminate theta between the equation : x =a cos theta + b sin theta, y =a sin theta- b cos theta .

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find dy/dx : x = cos theta - cos 2theta, y = sin theta - sin 2theta