find,in terms of pi,all the values of x between 0 and pi which satisfy the equation tan x +cot x =8cos2x
+128408 tan x +cot x =8cos2x
sin(x) / cos (x) + cos(x) / sin(x) = 8cos (2x)
sin^2(x) + cos^2(x) / [ sin(x)cos(x)] = 8cos(2x)
1 / [sin(x)cos(x)] = 8cos(2x)
1/[ sin(2x)/2 ] = 8cos(2x)
2 / sin(2x) = 8sos(2x)
1/ sin(2x) = 4cos(2x)
1/4 = cos(2x)sin(2x)
1/4 = (1/2)sin(4x)
2/4 = sin(4x)
1/2 = sin(4x)
sin (4x) = 1/2 when 4x = pi/6, 5pi/6, 13pi/6 and 17pi/6
so x = pi/24, 5pi/24, 13pi/24 and 17pi/24
