Solve {l}{(1+sinθ)(1-sinθ)/sin(90^{circ-θ)cos(90^circ-θ)tan(90^circ-θ)}}{(1-x^2)^2}

$$\left. \begin{array} { l } { \frac { ( 1 + \sin \theta ) ( 1 - \sin \theta ) } { \sin ( 90 ^ { \circ } - \theta ) \cos ( 90 ^ { \circ } - \theta ) \tan ( 90 ^ { \circ } - \theta ) } } \\ { ( 1 - x ^ { 2 } ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(x^{2}-1\right)^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$\left(1-x^{2}\right)^{2}=\left(x-1\right)^{2}\left(-x-1\right)^{2}$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x-1\right)^{2}\left(x+1\right)^{2}$$

Expand the expression.

$$x^{4}-2x^{2}+1$$

Evaluate

$$1,\left(1-x^{2}\right)^{2}$$