Bài tập 19 trang 200 SGK Toán 10 NC

a)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\sqrt {{{\sin }^4}\alpha  + {{\sin }^2}\alpha .{{\cos }^2}\alpha } \\
 = \sqrt {{{\sin }^2}\alpha \left( {{{\sin }^2}\alpha  + {{\cos }^2}\alpha } \right)} 
\end{array}\\
{ = \sqrt {{{\sin }^2}\alpha }  = \left| {\sin \alpha } \right|}
\end{array}\)

b)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\frac{{1 - \cos \alpha }}{{{{\sin }^2}\alpha }} - \frac{1}{{1 + \cos \alpha }}\\
 = \frac{{1 - \cos \alpha }}{{1 - {{\cos }^2}\alpha }} - \frac{1}{{1 + \cos \alpha }}
\end{array}\\
{ = \frac{1}{{1 + \cos \alpha }} - \frac{1}{{1 + \cos \alpha }} = 0}
\end{array}\)

c)

\(\begin{array}{l}
\frac{{1 - {{\sin }^2}\alpha .{{\cos }^2}\alpha }}{{{{\cos }^2}\alpha }} - {\cos ^2}\alpha \\
 = \frac{1}{{{{\cos }^2}\alpha }} - {\sin ^2}\alpha  - {\cos ^2}\alpha \\
 = \frac{1}{{{{\cos }^2}\alpha }} - 1 = {\tan ^2}\alpha 
\end{array}\)

-- Mod Toán 10 HỌC247