The functions $c(x)$ and $s(x)$ are defined by

1. Show that $c(x)$ is an even function and $s(x)$ is an odd function.

2. Show that

   $$s(2x)=2s(x)c(x)$$

3. Show that

   $$c(x{)}^2-s(x{)}^2=1$$

4. Solve the equation

   $$c(x{)}^2-s(x)=1,x>0$$

   giving your solution in the form

   $${\log }_2(a+\sqrt{b})$$

For (a), remember that a function $f$ is even if you can show that $f(x)=f(-x)$ for all $x$.

Similarly, to show a function is odd we need to show that $f(-x)=-f(x)$ for all $x$.

For (b), work out the left hand side and the right hand side separately and conclude that they are the same.

For (c), start with the left hand side.

For(d), use part (c) to change $c(x{)}^2$ into something in terms of $s(x{)}^2$.

For your solution to (d), give the value of