16cos^5 A+2 cosA-cos^3 A-cos5A=16cos^3 A
You asked:
Solve the equation \(16 {\cos\left( A \right)}^{5} + 2 \cos\left( A \right) - {\cos\left( A \right)}^{3} - \cos\left( 5 A \right) = 16 {\cos\left( A \right)}^{3}\) for the variable \(A\).
MathBot Answer:
The real solutions are: \[\begin{aligned}A &= \left\{2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n\; \middle|\; n \in \mathbb{Z}\right\}\\A &= \left\{\pi \left(1 + 2 n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.1415927\; \middle|\; n \in \mathbb{Z}\right\}\\A &= \left\{\frac{\pi \left(1 + 4 n\right)}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.5707963\; \middle|\; n \in \mathbb{Z}\right\}\\A &= \left\{\frac{\pi \left(3 + 4 n\right)}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.712389\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]