I have no idea where to start.
For the first one, I did the tan(a-b)=tan(a)+tan(b)/1+tan(a)tan(b), but I got -tan(x)/1.
Tangent isn't defined at . The identity doesn't seem possible in my opinion. Secant also is not defined at .
Edit: I was wrong, the identities DO seem to be true. I was mistaken because when I went to prove it with the tangent of a difference, the is undefined. What you need to do, is write the tangent as . So when you expand, all of the functions are defined on
For csc and the sec part
I did csc(pi/2-x)= 1/sin(pi/2-x) then I changed it to
1/ sin(pi/2)cos(x)-cos(pi/2)sin(x)= 1/cosx = sec(x)
I did it almost the same, but I didn't put pi/2-x on the numerator and denominator like how you did for tan. Did I do it wrong?
To do prove the cofunction theorem for cosecant, just expand:
If you expand this, you should get .