Bài tập 19 trang 200 SGK Toán 10 NC
Bài tập 19 trang 200 SGK Toán 10 NC
Đơn giản biểu thức
a) \(\sqrt {{{\sin }^4}\alpha + {{\sin }^2}\alpha .{{\cos }^2}\alpha } \)
b) \(\frac{{1 - \cos \alpha }}{{{{\sin }^2}\alpha }} - \frac{1}{{1 + \cos \alpha }}\)
c) \(\frac{{1 - {{\sin }^2}\alpha .{{\cos }^2}\alpha }}{{{{\cos }^2}\alpha }} - {\cos ^2}\alpha \left( {\cos \alpha \ne 0} \right)\)
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
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