7/sintheta-3costheta/sintheta=77sinθ−3cosθsinθ=7
7-3costheta = 7sintheta7−3cosθ=7sinθ
Put X=costhetaX=cosθ and Y=sinthetaY=sinθ then X^2+Y^2=1X2+Y2=1 and 7-3X=7Y7−3X=7Y
so X^2+(1-3/7X)^2=1X2+(1−37X)2=1
X^2+cancel(1)+9/49X^2-6/7X=cancel(1)
X=0 or 58/7X=6 => X=21/29
The solution X=0 gives theta=pi/2 so
7cot (pi/2)-3csc(pi/2)=0-3=-3
For theta=arccos(21/29) then costheta=21/29, sintheta=20/29
so
7costheta/sintheta-3/sintheta=((7*21)/29-3)/(20/29)=(147-87)/20=3