(sin2X +sin2Y)/(Cos2X+cos2Y) is identical to tan(X+Y)
2007-05-04 20:21:27 · 3 answers · asked by torpedo 1 in Science & Mathematics ➔ Mathematics
sinA + sinB = 2 sin (A + B)/2 cos (A-B)/2
cosA + cosB = 2 cos(A+B)/2 cos(A-B)/2
so
sin2X + sin2Y = 2sin (2X+2Y)/2 cos(2X-2Y)/2 = 2sin(X+Y)cos(X-Y)
cos2X + cos2Y= 2cos(2X+2Y)/2 cos(2X-2Y)/2 = 2cos(X+Y)cos(X-Y)
(sin2X + sin2Y)/ (cos2X + cos2Y) = sin(X + Y)/cos(X + Y) = tan(X + Y)
2007-05-04 20:49:58 · answer #1 · answered by fred 5 · 1⤊ 0⤋
= [2 sin (x + y) cos 0 ] / [2 cos (x + y) cos 0]
= 2 sin (x + y) / 2 cos (x + y)
= tan (x + y)
2007-05-05 03:37:01 · answer #2 · answered by Como 7 · 0⤊ 1⤋
2sin(x+y)cos(x-y)/(2)cos(x+y)cos(x-y)=
2 and 2 cancel out, cos(x-y) also cancel out. we get
sin(x+y)/cos(x+y)= tan(x+y).
proved.
2007-05-05 03:31:50 · answer #3 · answered by Anonymous · 0⤊ 0⤋