Prove Trigonometric Identities

David Cohen questions just for fun.
Enjoy.

 

is not true statement


tan(x/2)=(1-cos(x)+sin(x))/(1+cos(x)+sin(x))

manipulate right side
(1-cos(x)+sin(x))/(1+cos(x)+sin(x))............ 1-cos(x)=2sin^2(x/2), 1+cos(x)=2cos^2(x/2)

=(2sin^2(x/2)+sin(x))/(2cos^2(x/2)+sin(x))

=(2 sqrt(2) sin(x/2 + π/4) sin(x/2))/(2sqrt(2) sin(x/2 + π/4) cos(x/2))

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

= tan(x/2)

 

Don't you just love that Cohen Textbook?
Can you set up the second trigonometric identity for me to try on my own?

How about this one?

Find Speed

 

Prove the identity
cot(x) / csc(x) = cos(x)

 

Cool. I will work it out on paper and post here is necessary.