Bài tập 22 trang 201 SGK Toán 10 NC

a) Ta có

\(\begin{array}{*{20}{l}}
\begin{array}{l}
VT = {\cos ^4}\alpha  - {\sin ^4}\alpha \\
 = \left( {{{\cos }^2}\alpha  + {{\sin }^2}\alpha } \right).\left( {{{\cos }^2}\alpha  - {{\sin }^2}\alpha } \right)\\
 = {\cos ^2}\alpha  - {\sin ^2}\alpha 
\end{array}\\
\begin{array}{l}
 = {\cos ^2}\alpha  - \left( {1 - {{\cos }^2}\alpha } \right)\\
 = 2{\cos ^2}\alpha  - 1 = VP
\end{array}
\end{array}\)

b)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
VT = 1 - {\cot ^4}\alpha \\
 = \left( {1 + {{\cot }^2}\alpha } \right).\left( {1 - {{\cot }^2}\alpha } \right)
\end{array}\\
\begin{array}{l}
 = \frac{1}{{{{\sin }^2}\alpha }}\left( {\frac{{{{\sin }^2}\alpha  - \left( {1 - {{\sin }^2}\alpha } \right)}}{{{{\sin }^2}\alpha }}} \right)\\
 = \frac{{2{{\sin }^2}\alpha  - 1}}{{{{\sin }^4}\alpha }} = \frac{2}{{{{\sin }^2}\alpha }} - \frac{1}{{{{\sin }^4}\alpha }} = VP
\end{array}
\end{array}\)

c) 

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

-- Mod Toán 10 HỌC247