2.33*ln $\sqrt{1+cos^2(x)}$ /(e^y + sin^2(x))

asked by guest
on Sep 20, 2024 at 2:42 am



You asked:

Evaluate the expression: \(\frac{2.33 \cdot \ln\left( \sqrt{1 + {\cos\left( x \right)}^{2}} \right)}{{e}^{y} + {\sin\left( x \right)}^{2}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{2.33 \cdot \ln\left( \sqrt{1 + {\cos\left( x \right)}^{2}} \right)}{{e}^{y} + {\sin\left( x \right)}^{2}} = \frac{233 \log{\left(\sqrt{\cos^{2}{\left(x \right)} + 1} \right)}}{100 \left(e^{y} + \sin^{2}{\left(x \right)}\right)} \)

Expanded

\[\frac{2.33 \cdot \ln\left( \sqrt{1 + {\cos\left( x \right)}^{2}} \right)}{{e}^{y} + {\sin\left( x \right)}^{2}} = \frac{233 \log{\left(\cos^{2}{\left(x \right)} + 1 \right)}}{200 e^{y} + 200 \sin^{2}{\left(x \right)}}\]

Factored

\[\frac{2.33 \cdot \ln\left( \sqrt{1 + {\cos\left( x \right)}^{2}} \right)}{{e}^{y} + {\sin\left( x \right)}^{2}} = \frac{233 \log{\left(\cos^{2}{\left(x \right)} + 1 \right)}}{200 \left(e^{y} + \sin^{2}{\left(x \right)}\right)}\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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