cos(3*pi/8-x*1/4)^2-cos(11*pi/8+x*1/4)^2 если x=-1/3 (упростите выражение)

$$cos^{2}{left (- frac{x}{4} + frac{3 pi}{8} right )} – cos^{2}{left (frac{x}{4} + frac{11 pi}{8} right )}$$

$$cos^{2}{left (- frac{x}{4} + frac{3 pi}{8} right )} – cos^{2}{left (frac{x}{4} + frac{11 pi}{8} right )}$$

cos((3*pi)/8 – (-1/3)/4)^2 – cos((11*pi)/8 + (-1/3)/4)^2

$$cos^{2}{left (- frac{(-1/3)}{4} + frac{3 pi}{8} right )} – cos^{2}{left (frac{(-1/3)}{4} + frac{11 pi}{8} right )}$$

cos((3*pi)/8 – (-1)/(3*4))^2 – cos((11*pi)/8 – 1/12)^2

$$- cos^{2}{left (- frac{1}{12} + frac{11 pi}{8} right )} + cos^{2}{left (- frac{-1}{12} + frac{3 pi}{8} right )}$$

cos(1/12 + 3*pi/8)^2 – sin(1/12 + pi/8)^2

$$- sin^{2}{left (frac{1}{12} + frac{pi}{8} right )} + cos^{2}{left (frac{1}{12} + frac{3 pi}{8} right )}$$

$$sin^{2}{left (frac{x}{4} + frac{pi}{8} right )} – cos^{2}{left (frac{x}{4} + frac{3 pi}{8} right )}$$

cos((3*pi)/8 – x/4)^2 – cos((11*pi)/8 + x/4)^2

$$sin^{2}{left (frac{x}{4} + frac{pi}{8} right )} – cos^{2}{left (frac{x}{4} + frac{3 pi}{8} right )}$$

$$cos^{2}{left (frac{1}{8} left(- 2 x + 3 piright) right )} – cos^{2}{left (frac{1}{8} left(2 x + 11 piright) right )}$$

___ /x
/ 2 *sin|-|
2/
————
2

$$frac{sqrt{2}}{2} sin{left (frac{x}{2} right )}$$

$$frac{1}{2} sin{left (frac{x}{2} + frac{pi}{4} right )} – frac{1}{2} cos{left (frac{x}{2} + frac{pi}{4} right )}$$

2/x pi 2/x 3*pi
sin |- + –| – cos |- + —-|
4 8 / 4 8 /

$$sin^{2}{left (frac{x}{4} + frac{pi}{8} right )} – cos^{2}{left (frac{x}{4} + frac{3 pi}{8} right )}$$

___________ ___________
/ ___ / ___ /x
/ 2 + / 2 */ 2 – / 2 *sin|-|
2/
————————————
2

$$frac{1}{2} sqrt{- sqrt{2} + 2} sqrt{sqrt{2} + 2} sin{left (frac{x}{2} right )}$$

/ /x pi /x 3*pi / /x 3*pi /x pi
-|- sin|- + –| + cos|- + —-||*|cos|- + —-| + sin|- + –||
4 8 / 4 8 // 4 8 / 4 8 //

$$- left(- sin{left (frac{x}{4} + frac{pi}{8} right )} + cos{left (frac{x}{4} + frac{3 pi}{8} right )}right) left(sin{left (frac{x}{4} + frac{pi}{8} right )} + cos{left (frac{x}{4} + frac{3 pi}{8} right )}right)$$

2 2
/ ___________ ___________ / ___________ ___________
| / ___ / ___ | | / ___ / ___ |
| / 1 / 2 /x / 1 / 2 /x| | / 1 / 2 /x / 1 / 2 /x|
| / – – —– *cos|-| + / – + —– *sin|-|| – | / – + —– *sin|-| – / – – —– *cos|-||
/ 2 4 4/ / 2 4 4// / 2 4 4/ / 2 4 4//

$$- left(sqrt{frac{sqrt{2}}{4} + frac{1}{2}} sin{left (frac{x}{4} right )} – sqrt{- frac{sqrt{2}}{4} + frac{1}{2}} cos{left (frac{x}{4} right )}right)^{2} + left(sqrt{frac{sqrt{2}}{4} + frac{1}{2}} sin{left (frac{x}{4} right )} + sqrt{- frac{sqrt{2}}{4} + frac{1}{2}} cos{left (frac{x}{4} right )}right)^{2}$$