how to solve tan5x equal to tan2x

asked by guest
on Nov 20, 2024 at 1:11 am



You asked:

Solve the equation \(\tan\left( 5 x \right) = \tan\left( 2 x \right)\) for the variable \(x\).

MathBot Answer:

The real solutions are: \[\begin{aligned}x &= \left\{2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi \left(1 + 2 n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.1415927\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{2 \pi \left(2 + 3 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.1887902\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{2 \pi \left(1 + 3 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.0943951\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(5 + 6 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.2359878\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(1 + 6 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.0471976\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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