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Prove the trig identity: 1+cos x/sin x = csc x + cot x
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Answer to a math question Prove the trig identity: 1+cos x/sin x = csc x + cot x
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1. Start with the right-hand side of the equation: \csc x + \cot x
2. Express \csc x \cot x
\csc x = \frac{1}{\sin x}
\cot x = \frac{\cos x}{\sin x}
3. Add the fractions:
\csc x + \cot x = \frac{1}{\sin x} + \frac{\cos x}{\sin x} = \frac{1 + \cos x}{\sin x}
4. The expression \frac{1 + \cos x}{\sin x}
Therefore, the identity is valid:
\frac{1 + \cos x}{\sin x} = \csc x + \cot x
2. Express
3. Add the fractions:
4. The expression
Therefore, the identity is valid:
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