sinx=2sin(x/2)*cos(x/2)

cosx+ 1=[cos(x/2)]^2-[sin(x/2)]^2

+[cos(x/2)]^2+[sin(x/2)]^2

=2[cos(x/2)]^2

∴sinx/( 1+cosx)= 2sin(x/2)*cos(x/2)/2[cos(x/2)]^2=tanx/2= 1/2

tanx=2tan(x/2)/[ 1-tan^2(x/2)]=2* 1/2/[ 1- 1/4]= 4/3

2.cos20×cos40×cos60×cos80=？

cos20×cos40×cos60×cos80

= sin 20×cos 20×cos 40×cos 60×cos 80/sin 20

= sin 40×cos 40×cos 60×cos 80/2s in 20

=sin80×cos60×cos80/4sin20

=sin 160×cos60/8sin20

=sin20×cos60/8sin20

=cos60/8= 1/ 16

Because cos60= 1/2, the angle doubling formula is used step by step.

3. Simplify sin 130 degrees (1+ root number 3 times tan 10 degrees)

=sin50( 1+√3tan 10)

= sin 50(cos 10+√3 sin 10)/cos 10

= sin 50 * 2s in( 10+30)/cos 10

=2sin50sin40/cos 10

=2sin50cos50/cos 10

=sin 100/cos 10

=sin80/cos 10

=cos 10/cos 10

= 1