Simplify (csc(t))/(sec(t))

Problem

csc(t)/sec(t)

Solution

1. Use reciprocal identities to rewrite the trigonometric functions in terms of sine and cosine.

csc(t)=1/sin(t)

sec(t)=1/cos(t)

2. Substitute these identities into the original expression.

1/sin(t)/1/cos(t)

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

1/sin(t)⋅cos(t)/1

4. Multiply the fractions together.

cos(t)/sin(t)

5. Apply the quotient identity for the cotangent function.

cot(t)=cos(t)/sin(t)

Final Answer

csc(t)/sec(t)=cot(t)

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