show that tan(x)/sec2(x) = (1/2)sin(2x)

tan(x)/sec²(x) Sec(x) = 1/cos(x), therefore 1/sec(x) = cos(x). also tan(x) = sin(x)/cos(x).using substitution, tan(x)/sec²(x) = (sin(x)/cos(x)) * cos²(x) = sin(x)cos(x). sin(x+y) = sin(x)cos(y) + cos(x)sin(y). since 2x = x+x, sin(2x) = 2sin(x)cos(x). therefore, sin(x)cos(x) = (1/2)sin(2x)