Simplify (sec(x-1)^2)/(sin(x)^2)

Problem

sec(x−1)/sin(x)

Solution

1. Identify the expression as a quotient of a squared secant function and a squared sine function.

2. Apply the reciprocal identity for secant, where sec(θ)=1/cos(θ)

3. Substitute the identity into the numerator to rewrite the expression in terms of sine and cosine.

4. Simplify the fraction by moving the cosine term to the denominator.

Final Answer

sec(x−1)/sin(x)=1/(sin(x)*cos(x−1))

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