Answer:
To solve the given trigonometric equation, we can start by isolating the cos(theta) term on one side of the equation. We can do this by dividing both sides of the equation by csc(theta):cos(theta) * csc(theta) - 2cos(theta) = 0
cos(theta) * csc(theta) / csc(theta) - 2cos(theta) / csc(theta) = 0 / csc(theta)
cos(theta) - 2cos(theta) / csc(theta) = 0Next, we can combine like terms on the left side of the equation:cos(theta) - 2cos(theta) / csc(theta) = 0
-2cos(theta) / csc(theta) + cos(theta) = 0
(1 - 2 / csc(theta)) cos(theta) = 0Since cos(theta) cannot be equal to 0 (because the angle theta is between 0 and 2pi), the only solution to this equation is:1 - 2 / csc(theta) = 0
1 = 2 / csc(theta)
csc(theta) = 2This means that the value of csc(theta) is equal to 2. To find the value of theta, we can use the inverse cosecant function (arcsec) to solve for theta:theta = arcsec(2)The value of arcsec(2) is approximately 1.047198, which is the solution to the given equation for theta.Note that this is just one solution to the equation, as there may be other solutions for theta depending on the values of the trigonometric functions. It is important to check that the solution falls within the given range of 0 < theta < 2pi.