" If "(sin(x/2)+cos(x/2)+i tan x)/(1+2i sin(x/2))" is real then "x

If the expression (sin(x/2)+cos(x/2)-i tan(x/2))/(1+2isin(x/2)) is real, the find the set of al possible values of x

If the expression ([sin((x)/(2))+cos((x)/(2))-i tan(x)])/([1+2i sin((x)/(2))]) is real,then the set of all possible values of x is.......

(sin2x)/(1+cos2x)=tan x

Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)

I=int(sin^(2)x-cos^(2)x)/(sin^(2)x*cos^(2)x)dx

I =int (sin ^(8) x- cos ^(8) x)/( 1-2 sin ^(2) x cos ^(2)x ) dx is equal to:

Find real x such that (3+2i sin x)/(1-2i sin x) is purely real.