SOLUTION: solve tanx cosx= 1/2 for all values of x.

Question 816116: solve tanx cosx= 1/2 for all values of x.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

One way to solve this is to start by replacing tan with sin/cos:

The cos's cancel:

We should recognize that 1/2 is a special angle value for sin. It tells us that the reference angle is . Since the 1/2 is positive and sin is positive in the 1st and 2nd quadrants, we should get the following general solution equations:
(for the 1st quadrant)
(for the 2nd quadrant)
The second equation will simplify:

The problem asks for all values of x. This is what the general solution is. So all the solutions are described by:

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