Lane Gough
08/11/2024 · Senior High School
\( \operatorname { tag } \theta \cdot \operatorname { cic } \theta \)
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The expression you've written, \( \operatorname{tag} \theta \cdot \operatorname{cic} \theta \), seems to involve trigonometric functions, but the terms "tag" and "cic" are not standard notations in trigonometry.
If you meant to refer to the tangent and secant functions, the correct notation would be:
- \( \tan \theta \) for tangent
- \( \sec \theta \) for secant
In that case, the expression would be:
\[
\tan \theta \cdot \sec \theta
\]
Using the definitions of these functions, we have:
\[
\tan \theta = \frac{\sin \theta}{\cos \theta}
\]
\[
\sec \theta = \frac{1}{\cos \theta}
\]
Thus, the product becomes:
\[
\tan \theta \cdot \sec \theta = \frac{\sin \theta}{\cos \theta} \cdot \frac{1}{\cos \theta} = \frac{\sin \theta}{\cos^2 \theta}
\]
If "tag" and "cic" refer to something else, please clarify, and I would be happy to help further!
Quick Answer
The expression simplifies to \( \frac{\sin \theta}{\cos^2 \theta} \).
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