Simplified Expression: -tan(x)/(1 + cot^2(x)) + c

-cot x + c

To understand how to simplify the expression -cot(x) + c, let’s break it down step by step

To understand how to simplify the expression -cot(x) + c, let’s break it down step by step.

First, recall that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1/tan(x)

So, substituting this in the expression, we have:

-cot(x) + c = – (1/tan(x)) + c

Next, let’s find a common denominator for -1 and tan(x), which is tan(x):

– (1/tan(x)) + c = – (1/tan(x)) * (tan(x)/tan(x)) + c

Simplifying further, we get:

– (1/tan(x)) * (tan(x)/tan(x)) + c = – tan(x)/(tan(x) * tan(x)) + c

Since tan(x) * tan(x) is equal to tan^2(x), we can rewrite the expression as:

– tan(x)/(tan^2(x)) + c

Finally, we can simplify the expression further. Since tan^2(x) is equivalent to 1 + cot^2(x), we have:

– tan(x)/(tan^2(x)) + c = – tan(x)/(1 + cot^2(x)) + c

Therefore, the simplified expression is:

-cot(x) + c simplifies to -tan(x)/(1 + cot^2(x)) + c.

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