\operatorname { lan } ^ { 2 } ( \frac { 1 } { 2 } + \alpha ) [ 1 - \sin ^ { 2 } ( \alpha - \frac { 1 } { 2 } ) ] + \cos ^ { 2 } ( \frac { 1 } { 2 }
Factor
\frac{\left(2\alpha +1\right)\left(aln\right)^{2}\left(-\left(\sin(\frac{2\alpha -1}{2})\right)^{2}+1\right)+2\left(\cos(\frac{1}{2})\right)^{2}}{2}
Evaluate
\frac{\left(2\alpha +1\right)\left(aln\right)^{2}\left(-\left(\sin(\frac{2\alpha -1}{2})\right)^{2}+1\right)+2\left(\cos(\frac{1}{2})\right)^{2}}{2}
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\frac{\left(lan\right)^{2}\left(1+2\alpha \right)\left(1-\left(\sin(\frac{2\alpha -1}{2})\right)^{2}\right)+2\left(\cos(\frac{1}{2})\right)^{2}}{2}
Factor out \frac{1}{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}