Solve for x (in radians) if cosec(2x)=2

Sure, let's solve the equation step by step.

The cosecant function, csc(x), is defined as 1/sin(x). So, if csc(2x) = 2, then 1/sin(2x) = 2.

Step 1: Rewrite the equation in terms of sine: 1/sin(2x) = 2 This implies that sin(2x) = 1/2.

Step 2: Solve for 2x: The solutions to sin(x) = 1/2 are x = π/6 + nπ, x = 5π/6 + nπ, where n is an integer. Therefore, the solutions to sin(2x) = 1/2 are 2x = π/6 + nπ, 2x = 5π/6 + nπ.

Step 3: Solve for x: Divide each side of the equation by 2 to solve for x. The solutions are x = π/12 + nπ/2, x = 5π/12 + nπ/2.

So, the solutions to the equation csc(2x) = 2 are x = π/12 + nπ/2, x = 5π/12 + nπ/2, where n is an integer.