| π | π | |||
Wykaż, że funkcja f(x)=cos2x+cos2( | +x)−cosxcos( | +x) jest funkcją stałą. | ||
| 3 | 3 |
| π | π | π | 1 | √3 | ||||||
cos( | +x)=cos( | )cos(x)−sin( | )sin(x)= | cos(x)− | sin(x) | |||||
| 3 | 3 | 3 | 2 | 2 |
| 1 | √3 | 1 | √3 | |||||
f(x)=cos2(x)+( | cos(x)− | sin(x))2−cos(x)( | cos(x)− | sin(x))= | ||||
| 2 | 2 | 2 | 2 |
| 1 | √3 | 3 | 1 | |||||
=cos2(x)+ | cos2(x)− | sin(x)cos(x)+ | sin2(x)− | cos2(x)+ | ||||
| 4 | 2 | 4 | 2 |
| √3 | 3 | 3 | ||||
+ | sin(x)cos(x)= | (cos2(x)+sin2(x))= | ||||
| 2 | 4 | 4 |