Sin x + cot x
Understand the Problem
The question is asking for the expression 'sin x + cot x', which involves understanding the sine and cotangent functions in trigonometry. To solve or simplify this expression, one might consider using trigonometric identities or converting the cotangent into sine and cosine terms.
Answer
$$ \frac{\sin^2 x + \cos x}{\sin x} $$
Answer for screen readers
The expression simplified is
$$ \frac{\sin^2 x + \cos x}{\sin x} $$
Steps to Solve
- Rewrite cotangent in terms of sine and cosine
The cotangent function is defined as the ratio of cosine to sine:
$$ \cot x = \frac{\cos x}{\sin x} $$
Thus, we can rewrite the expression as:
$$ \sin x + \cot x = \sin x + \frac{\cos x}{\sin x} $$
- Combine the terms into a single fraction
To combine the terms, we need a common denominator:
$$ \sin x + \frac{\cos x}{\sin x} = \frac{\sin^2 x + \cos x}{\sin x} $$
- Simplify the expression if necessary
The final expression we derived is:
$$ \frac{\sin^2 x + \cos x}{\sin x} $$
This is the simplified form of the original expression.
The expression simplified is
$$ \frac{\sin^2 x + \cos x}{\sin x} $$
More Information
This expression combines both sine and cotangent into a single fraction. The cotangent function relates to the sine and cosine functions through identities, making it possible to express trigonometric functions in various forms.
Tips
- Confusing cotangent with tangent: Remember, cotangent is the reciprocal of tangent, so it's important to use the correct definition: $ \cot x = \frac{\cos x}{\sin x} $.
- Forgetting to find a common denominator when combining fractions.
