Verify the Identity csc(2x)=(csc(x))/(2cos(x))

Problem

csc(2*x)=csc(x)/(2*cos(x))

Solution

1. Identify the double angle identity for the sine function, since csc(2*x)=1/sin(2*x)

2. Substitute the identity sin(2*x)=2*sin(x)*cos(x) into the left side of the equation.

csc(2*x)=1/sin(2*x)

csc(2*x)=1/(2*sin(x)*cos(x))

3. Rewrite the expression by recognizing that 1/sin(x)=csc(x)

csc(2*x)=1/sin(x)⋅1/(2*cos(x))

4. Simplify the product to match the right side of the identity.

csc(2*x)=csc(x)/(2*cos(x))

Final Answer

csc(2*x)=csc(x)/(2*cos(x))

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