(Solved): Consider the two polar curves \[ C_{1}: r=1+\cos \theta \quad \text { and } \quad C_{2}: r=2-\cos ...

Consider the two polar curves \[ C_{1}: r=1+\cos \theta \quad \text { and } \quad C_{2}: r=2-\cos \theta \] a) Find the equation of the tangent to the curve \( r=1+\cos \theta \) at \( \theta=\frac{\pi}{2} \).(5 points) b) Set up a definite integral that computes the area of the region that lies inside the curve \( r=1+\cos \theta \) and outside the curve \( r=2-\cos \theta \). Do not evaluate the definite integral. (3 points) c) Set up a definite integral that computes the length of the polar curve \( r=2-\cos \theta \) that is outside the curve \( r=1+\cos \theta \). Do not evaluate the definite integral. (3 points)