Jimenez Weston
08/07/2024 · High School
simplificar la exprec \( \frac{\sec x \cot }{\tan x} \)
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Step-by-step Solution
Calculate or simplify the expression \( \frac{\sec(x) \cdot \cot(x)}{\tan(x)} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\sec\left(x\right)\cot\left(x\right)}{\tan\left(x\right)}\)
- step1: Transform the expression:
\(\frac{\frac{\cot\left(x\right)}{\cos\left(x\right)}}{\tan\left(x\right)}\)
- step2: Multiply by the reciprocal:
\(\frac{\cot\left(x\right)}{\cos\left(x\right)}\times \frac{1}{\tan\left(x\right)}\)
- step3: Multiply the terms:
\(\frac{\cot\left(x\right)}{\cos\left(x\right)\tan\left(x\right)}\)
- step4: Transform the expression:
\(\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)\tan\left(x\right)}\)
- step5: Transform the expression:
\(\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\sin\left(x\right)}\)
- step6: Multiply by the reciprocal:
\(\frac{\cos\left(x\right)}{\sin\left(x\right)}\times \frac{1}{\sin\left(x\right)}\)
- step7: Multiply the terms:
\(\frac{\cos\left(x\right)}{\sin\left(x\right)\sin\left(x\right)}\)
- step8: Multiply the terms:
\(\frac{\cos\left(x\right)}{\sin^{2}\left(x\right)}\)
- step9: Transform the expression:
\(\cos\left(x\right)\csc^{2}\left(x\right)\)
La expresión simplificada es \( \cos(x) \csc^2(x) \).
Quick Answer
Expresión simplificada: \( \cos(x) \csc^2(x) \)
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