Question 816116
{{{tan(x)cos(x) = 1/2}}}
One way to solve this is to start by replacing tan with sin/cos:
{{{(sin(x)/cos(x))cos(x) = 1/2}}}
The cos's cancel:
{{{sin(x) = 1/2}}}
We should recognize that 1/2 is a special angle value for sin. It tells us that the reference angle is {{{pi/6}}}. Since the 1/2 is positive and sin is positive in the 1st and 2nd quadrants, we should get the following general solution equations:
{{{x = pi/6 + 2pi*n}}} (for the 1st quadrant)
{{{x = pi-pi/6 + 2pi*n}}} (for the 2nd quadrant)
The second equation will simplify:
{{{x = 5pi/6 + 2pi*n}}}<br>
The problem asks for all values of x. This is what the general solution is. So all the solutions are described by:
{{{x = pi/6 + 2pi*n}}}
{{{x = 5pi/6 + 2pi*n}}}