Question

question. simplify to a single trig function with no denominator.
\frac{\sec ^{2}x}{\csc ^{2}x - \cot ^{2}x}
answer attempt 1 out of 2
answer:
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Explanation:

Step1: Use Pythagorean identity

We know the Pythagorean identity \( \csc^{2}x=1 + \cot^{2}x\). Substitute this into the numerator:

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Step2: Simplify the numerator

Simplify the numerator \((1+\cot^{2}x)-\cot^{2}x\). The \(\cot^{2}x\) terms cancel out, and we get \(\frac{1}{\sec^{2}x}\).

Step3: Use reciprocal identity

Since \(\cos x=\frac{1}{\sec x}\), then \(\frac{1}{\sec^{2}x}=\cos^{2}x\)

Answer:

\(\cos^{2}x\)