Bài tập 34 trang 207 SGK Toán 10 NC

a)

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

b)

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

c)

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

-- Mod Toán 10 HỌC247