Solve for x in the equation:tan x=2sin x for -180<=x<=180

Answer 1

To solve the equation tan(x) = 2sin(x), we can rewrite it in terms of sine and cosine using the identity: tan(x) = sin(x)/cos(x).

Therefore, we have: sin(x)/cos(x) = 2sin(x).

Multiplying both sides by cos(x), we get: sin(x) = 2sin(x)cos(x).

Dividing both sides by sin(x), we have: 1 = 2cos(x).

Dividing both sides by 2, we get: 1/2 = cos(x).

So, x = arccos(1/2).

Using a calculator to find the inverse cosine of 1/2, we get two possible solutions:
x = 60 degrees or x = 300 degrees.

However, the range given is -180 degrees to 180 degrees. Therefore, the only solution in that range is x = 60 degrees.