How can I be sure if I can apply a function to both sides of an equation and preserve equality?
for example:
x = y ⇔ x2 = y2
or
x = y ⇔ \sqrt{}x = \sqrt{}y
or
x < y ⇔ log(x) < log(y)
What's up with that?
Homework Statement
Prove sinx/(2sin(x/2)) = cos(x/2)
and
(sin(x) cos(x/2^(n+1)))/(2^n(sinx/2^n)) = sinx/(2^(n+1)sin(x/(2^n+1)))
Homework Equations
The Attempt at a Solution