# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to\pi}\left(\frac{\ln\left(1+\sin\left(x\right)\right)}{\tan\left(x\right)}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to\pi }\left(\frac{\frac{d}{dx}\left(\ln\left(1+\sin\left(x\right)\right)\right)}{\frac{d}{dx}\left(\tan\left(x\right)\right)}\right)$

Learn how to solve limits problems step by step online. Evaluate the limit of (ln(1+sin(x))/(tan(x) as x approaches pi. As the limit results in indeterminate form, we can apply L'Hôpital's rule. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of the linear function is equal to 1. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.

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### Problem Analysis

$\lim_{x\to\pi}\left(\frac{\ln\left(1+\sin\left(x\right)\right)}{\tan\left(x\right)}\right)$

Limits

~ 0.07 seconds