Could someone please show me how

Question

1 / ( 4 tan (x/2) + 2 )

is converted to:
(- sin (x/2) /( 2 sin (x/2) + cos (x/2))

TIA
Carol

Answer 1

lets check it at x=0, and x=PI/2

x=0: 1/4(1+2)=1/12

(-sin45/(2sin45+cos45)=-.707/(1.414+.707) does not equal 1/12

Answer 2

that was at x=90 deg, the identity did not hold. Now at x=0

1/4(0+2)=1/8
-0/(0+.7) does not equal 1/8