Simplify (csc(theta))/(cot(theta))

Problem

csc(θ)/cot(θ)

Solution

1. Rewrite the numerator using the reciprocal identity for cosecant.

csc(θ)=1/sin(θ)

2. Rewrite the denominator using the quotient identity for cotangent.

cot(θ)=cos(θ)/sin(θ)

3. Substitute these identities into the original expression.

1/sin(θ)/cos(θ)/sin(θ)

4. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

1/sin(θ)⋅sin(θ)/cos(θ)

5. Cancel the common factor of sin(θ) from the numerator and the denominator.

1/cos(θ)

6. Apply the reciprocal identity for secant to find the final simplified form.

1/cos(θ)=sec(θ)

Final Answer

csc(θ)/cot(θ)=sec(θ)

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