Question

49.a) Prove geometrically that
cos(x + y) = cos X.cos y -- sin x.sin y​

Answer 1

Step-by-step explanation:

consider the circle with center at the origin. let x be angle p4op1 and y be the angle p1op2.then (x+y) is the angle p4op2. also let (-y)be the angle p4op3. therefore,p1,p2,p3 and p4 will have the coordinates p1(cosx,sinx),p2[cos(x+y),sin(x+y)],p3[cos(-y),sin(-y)]&p4(1,0) in that figure

consider the triangles P1OP3 and p2op4. They are congruent. therefore , p1p3 and p2p4 are equal.by using distance formula,we get

remaining there in 2nd and 3rd fig