Simplify (1-sin^2(t))/(sin^2)(t) to an expression involving a single squared trig function with no __

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Answer 1

To simplify the expression \(\frac{1 - \sin^2(t)}{\sin^2(t)}\), we can use the Pythagorean identity for sine and cosine. The identity states:

From this identity, we can express \(1 - \sin^2(t)\) in terms of \(\cos^2(t)\):

Now, substitute \(\cos^2(t)\) into the original expression:

The resulting expression is:

This can be written as:

where \(\cot(t)\) is the cotangent function, which is the reciprocal of the tangent function.Thus, the simplified form of the given expression is:

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