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Resolver desigualdades/ sin(pi/4)*cos(x)+cos(pi/8)*sin(x)<=1

sin(pi/4)*cos(x)+cos(pi/8)*sin(x)<=1 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
   /pi\             /pi\            
sin|--|*cos(x) + cos|--|*sin(x) <= 1
   \4 /             \8 /
sin⁡(x)cos⁡(π8)+sin⁡(π4)cos⁡(x)≤1\sin{\left(x \right)} \cos{\left(\frac{\pi}{8} \right)} + \sin{\left(\frac{\pi}{4} \right)} \cos{\left(x \right)} \leq 1 
sin(x)*cos(pi/8) + sin(pi/4)*cos(x) <= 1
Solución de la desigualdad en el gráfico
0-60-50-40-30-20-101020304050602.5-2.5
Respuesta rápida 2 [src] 
[0, 2*pi]
x in [0,2π]x\ in\ \left[0, 2 \pi\right] 
x in Interval(0, 2*pi)
Respuesta rápida [src] 
  /   /                /      /                ___________   \      /       _____________________________\\\     /              /      /               ___________    \      /       _____________________________\\     \\
  |   |                |      |     3/4       /       ___    |      |      /                      ___    |||     |              |      |    3/4       /       ___     |      |      /                      ___    ||     ||
  |   |                |      |  - 2    + 2*\/  2 + \/ 2     |      |     /       18          8*\/ 2     |||     |              |      |   2    + 2*\/  2 + \/ 2      |      |     /       18          8*\/ 2     ||     ||
Or|And|0 <= x, x <= -I*|I*atan|------------------------------| + log|    /   ------------ + ------------ |||, And|x <= 2*pi, -I*|I*atan|------------------------------| + log|    /   ------------ + ------------ || <= x||
  |   |                |      |                   ___________|      |   /               2              2 |||     |              |      |                   ___________|      |   /               2              2 ||     ||
  |   |                |      |    ___   4 ___   /       ___ |      |  /     /      ___\    /      ___\  |||     |              |      |    ___   4 ___   /       ___ |      |  /     /      ___\    /      ___\  ||     ||
  \   \                \      \2*\/ 2  + \/ 2 *\/  2 + \/ 2  /      \\/      \4 + \/ 2 /    \4 + \/ 2 /  ///     \              \      \2*\/ 2  - \/ 2 *\/  2 + \/ 2  /      \\/      \4 + \/ 2 /    \4 + \/ 2 /  //     //
(0≤x∧x≤−i(log⁡(82(2+4)2+18(2+4)2)+iatan⁡(−234+22+2242+2+22)))∨(x≤2π∧−i(log⁡(82(2+4)2+18(2+4)2)+iatan⁡(234+22+2−242+2+22))≤x)\left(0 \leq x \wedge x \leq - i \left(\log{\left(\sqrt{\frac{8 \sqrt{2}}{\left(\sqrt{2} + 4\right)^{2}} + \frac{18}{\left(\sqrt{2} + 4\right)^{2}}} \right)} + i \operatorname{atan}{\left(\frac{- 2^{\frac{3}{4}} + 2 \sqrt{\sqrt{2} + 2}}{\sqrt[4]{2} \sqrt{\sqrt{2} + 2} + 2 \sqrt{2}} \right)}\right)\right) \vee \left(x \leq 2 \pi \wedge - i \left(\log{\left(\sqrt{\frac{8 \sqrt{2}}{\left(\sqrt{2} + 4\right)^{2}} + \frac{18}{\left(\sqrt{2} + 4\right)^{2}}} \right)} + i \operatorname{atan}{\left(\frac{2^{\frac{3}{4}} + 2 \sqrt{\sqrt{2} + 2}}{- \sqrt[4]{2} \sqrt{\sqrt{2} + 2} + 2 \sqrt{2}} \right)}\right) \leq x\right) 
((0 <= x)∧(x <= -i*(i*atan((-2^(3/4) + 2*sqrt(2 + sqrt(2)))/(2*sqrt(2) + 2^(1/4)*sqrt(2 + sqrt(2)))) + log(sqrt(18/(4 + sqrt(2))^2 + 8*sqrt(2)/(4 + sqrt(2))^2)))))∨((x <= 2*pi)∧(-i*(i*atan((2^(3/4) + 2*sqrt(2 + sqrt(2)))/(2*sqrt(2) - 2^(1/4)*sqrt(2 + sqrt(2)))) + log(sqrt(18/(4 + sqrt(2))^2 + 8*sqrt(2)/(4 + sqrt(2))^2))) <= x))
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