-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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