Find the exact value of cot(15degrees) using half angle formulas?

Double angle (or half angle, depending how you look at it) identities:

So we have

Note that when taking the square root, we should take into account that that could yield two possible solutions, but we know and , so it's also the case that .

Also, the reason we have equality in the last step can be explained like so:

(not unlike the process used to complete the square)

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph