Question
Complete the identity. \( \csc x(\sin x+\cos x)= \) ?
Ask by Graham Colon. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \csc x(\sin x+\cos x) = 1 + \cot x \)
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Beyond the Answer
To complete the identity, we start with the expression given: \(\csc x(\sin x + \cos x)\). Since \(\csc x = \frac{1}{\sin x}\), we can rewrite the expression as: \(\frac{1}{\sin x}(\sin x + \cos x)\). Distributing \(\frac{1}{\sin x}\) gives us: \(\frac{\sin x}{\sin x} + \frac{\cos x}{\sin x} = 1 + \cot x\). So, we have: \(\csc x(\sin x + \cos x) = 1 + \cot x\).
