```Question 615987
If 165 is double or half of a special angle then the answer is yes. With a little effort we should be able to answer this with: Yes. 165 = (1/2)(330) and 330 is a special angle. So:
Let x = 330/ Then (1/2)x = 165
Now we can use
{{{tan((1/2)x) = (1-cos(x))/sin(x)}}}
Replacing x with 330 and (1/2)x with 165 we get:
{{{tan(165) = (1-cos(330))/sin(330)}}}<br>
An angle of 330 degrees terminates in the 4th quadrant and has a reference angle of 30 degrees.
Since sin is negative in the 4th quadrant and since sin(30) = 1/2, sin(330) = -1/2.
Since cos is positive in the 4th quadrant and since cos(30) = {{{sqrt(3)/2}}}, cos(330) = {{{sqrt(3)/2}}}.
Substituting these into the formula we get:
{{{tan(165) = (1-(sqrt(3)/2))/(-1/2)}}}
Multiplying the top and bottom of the fraction by 2 will eliminate the "little" fractions:
{{{tan(165) = ((1-(sqrt(3)/2))/(-1/2))(2/2)}}}
which simplifies to:
{{{tan(165) = (2-sqrt(3))/-1}}}
{{{tan(165) = -2+sqrt(3)}}}
This is the exact value for tan(165).```