Step-by-step explanation:
[tex](1 + \cos(x) )(1 - \cos(x) )[/tex]
[tex]1 - \cos {}^{2} (x) [/tex]
[tex] = \sin {}^{2} (x) [/tex]
b.
[tex] \frac{1}{ \cot {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } [/tex]
[tex] \frac{1}{ \frac{ \cos {}^{2} (x) }{ \sin { }^{2} (x) } } - \frac{1}{ \cos {}^{2} (x) } [/tex]
[tex] \frac{1}{ \cot {}^{2} (x) } - \frac{ \csc {}^{2} (x) {} }{ \cot {}^{2} (x) } [/tex]
[tex] \frac{ - \cot {}^{2} (x) }{ \cot {}^{2} (x) } [/tex]
[tex] - 1[/tex]
c.
[tex] \sec {}^{2} ( \frac{\pi}{2} - x ) )( \sin {}^{2} (x) - \sin {}^{4} (x)) [/tex]
[tex]( \csc {}^{2} (x) )( \sin {}^{2} (x) - \sin {}^{4} (x ) [/tex]
[tex] \csc {}^{2} (x) ( \frac{1}{ \csc {}^{2} (x) } - \frac{1}{ \csc {}^{4} (x) } )[/tex]
[tex]1 - \frac{1}{ \csc {}^{2} (x) } [/tex]
[tex]1 - \sin {}^{2} (x) [/tex]
[tex] \cos {}^{2} (x) [/tex]
