Simplify csc(2x)

Problem

csc(2*x)

Solution

1. Identify the reciprocal identity for the cosecant function.

csc(θ)=1/sin(θ)

2. Substitute the argument 2*x into the reciprocal identity.

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

3. Apply the double angle formula for the sine function, which states sin(2*x)=2*sin(x)*cos(x)

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

4. Rewrite the expression using reciprocal identities 1/sin(x)=csc(x) and 1/cos(x)=sec(x) if a product form is desired.

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

Final Answer

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

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