Convert `r=cos e ctheta e^(rcostheta)` into its equivalent Cartesian equation.

Convert rsintheta=rcostheta+4 into its equivalent Cartesian equation.

Convert r=4tanthetasectheta into its equivalent Cartesian equation.

Convert the polar coordinates to its equivalent Cartesian coordinates (2,pi/2) .

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) (2,pi)

(b) Transfer the equation r=a cos theta of polar co-ordinates into an equation of Cartesian co-ordinates.

If cos e ctheta-cottheta=q , then the value of cos e ctheta is

If roots of equation 3x^2+5x+1=0 are (sectheta_1-t a ntheta_1) and (cos e ctheta_2-cottheta_2)dot Then find the equation whose roots are (sectheta_1+t a ntheta_1) and (cos e ctheta_2+cottheta_2)dot

(i) Find the vector equation of a line passing through a point with position vector 2hat(i)-hat(j)+hat(k) , and parallel to the line joining the points -hat(i)+4hat(j)+hat(k) and hat(i)+2hat(j)+2hat(k) . Also find the cartesian equivalent of this equation. (ii) The cartesian equations of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find vector equation of the line.

Two cells of emf E_1.E_2 and internal resistance r_1 , r_2 respectively are connected to parallel combination. Determine the equivalent emf of the combination.

If sinx+cos e cx=2, then sin^n x+cos e c^n x is equal to