sinx=sin2x
You asked:
Solve the equation \(\sin\left( x \right) = \sin\left( 2 x \right)\) for the variable \(x\).
MathBot Answer:
The real solutions are: \[\begin{aligned}x &= \left\{2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi \left(1 + 2 n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.1415927\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(5 + 6 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.2359878\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(1 + 6 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.0471976\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]