Final answer:
To solve the equation 2tan(x)csc(x)=3 for x in degrees, simplify the equation using reciprocal trigonometric identities, then isolate the variable x by performing mathematical operations.
Step-by-step explanation:
To solve the equation 2tan(x)csc(x)=3 for x in degrees, we need to isolate the variable x. First, simplify the equation by using the reciprocal trigonometric identities:
2tan(x)csc(x) = 2sin(x)/cos(x) * 1/sin(x) = 2/cos(x) = 3
Multiply both sides by cos(x): cos(x) * 2/cos(x) = 3 * cos(x)
Simplify further to get: 2 = 3cos(x)
Divide both sides by 3: 2/3 = cos(x)
Find the inverse cosine of both sides to solve for x: x = cos^(-1)(2/3)