tan(x)/cos(x)+1/(1+tan(x))=4/3

asked by guest
on Oct 25, 2024 at 4:16 am



You asked:

Solve the equation \(\frac{\tan\left( x \right)}{\cos\left( x \right)} + \frac{1}{1 + \tan\left( x \right)} = \frac{4}{3}\) for the variable \(x\).

MathBot Answer:

The real solutions are: \[\begin{aligned}x &= \left\{2 \arctan{\left(\operatorname{CRootOf} {\left(-1 + x^{6} - 14 x^{5} - 2 x + 9 x^{4} + 15 x^{2} + 16 x^{3}, 1\right)} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.54620426\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{2 \arctan{\left(\operatorname{CRootOf} {\left(-1 + x^{6} - 14 x^{5} - 2 x + 9 x^{4} + 15 x^{2} + 16 x^{3}, 2\right)} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.1302757\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{2 \arctan{\left(\operatorname{CRootOf} {\left(-1 + x^{6} - 14 x^{5} - 2 x + 9 x^{4} + 15 x^{2} + 16 x^{3}, 3\right)} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.9906094\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{2 \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(-1 + x^{6} - 14 x^{5} - 2 x + 9 x^{4} + 15 x^{2} + 16 x^{3}, 0\right)} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.856838\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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