Factor
\frac{\sqrt{2}\left(\sqrt[4]{2}\sqrt{\sqrt{2}+1}\cos(x)+\sqrt[4]{2}\sqrt{\sqrt{2}-1}\sin(x)-\sin(4x)+1\right)}{2}
Evaluate
\frac{\sqrt{2}\left(\sqrt{\sqrt{2}\left(\sqrt{2}+1\right)}\cos(x)+\sqrt{\sqrt{2}\left(\sqrt{2}-1\right)}\sin(x)-\sin(4x)+1\right)}{2}
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\sqrt{2}\left(\left(\sin(\frac{8x-\pi }{4})\right)^{2}+\cos(\frac{8x-\pi }{8})\right)
Factor out \sqrt{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}