(a) Use the identity for tansx 2 yd (see Equation 14b in

Chapter , Problem 21

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(a) Use the identity for tansx 2 yd (see Equation 14b in Appendix D) to show that if two lines L1 and L2 intersect at an angle , then tan m2 2 m1 1 1 m1m2 where m1 and m2 are the slopes of L1 and L2, respectively. (b) The angle between the curves C1 and C2 at a point of intersection P is defined to be the angle between the tangent lines to C1 and C2 at P (if these tangent lines exist). Use part (a) to find, correct to the nearest degree, the angle between each pair of curves at each point of intersection. (i) y x 2 and y sx 2 2d 2 (ii) x 2 2 y 2 3 and x 2 2 4x 1 y 2 1 3 0