Làm dùm em câu d , câu e cậu f vs ạ Question Làm dùm em câu d , câu e cậu f vs ạ in progress 0 Môn Toán Huy Gia 4 years 2020-10-28T22:41:28+00:00 2020-10-28T22:41:28+00:00 1 Answers 83 views 0
Answers ( )
Đáp án:
${d)x = \dfrac{\pi }{2} + k\pi ;x = \arctan \left( { – 3} \right) + k\pi \left( {k \in Z} \right)}$
${e)x = \arctan 3 + k\pi ;x = \arctan 7 + k\pi \left( {k \in Z} \right)}$
${f)x = \dfrac{\pi }{4} + k\pi ;x = \arctan 2 + k\pi \left( {k \in Z} \right)}$
Giải thích các bước giải:
$\begin{array}{l}
d)2{\cos ^2}x + \sin 2x – 4{\sin ^2}x = – 4\\
\Leftrightarrow 2{\cos ^2}x + \sin 2x – 4{\sin ^2}x + 4 = 0\\
\Leftrightarrow 2{\cos ^2}x + \sin 2x – 4{\sin ^2}x + 4\left( {{{\cos }^2}x + {{\sin }^2}x} \right) = 0\\
\Leftrightarrow 6{\cos ^2}x + 2\sin x\cos x = 0\\
\Leftrightarrow 2\cos x\left( {3\cos x + \sin x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
3\cos x + \sin x = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \left( {k \in Z} \right)\\
\sin x = – 3\cos x
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \left( {k \in Z} \right)\\
\tan x = – 3
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \\
x = \arctan \left( { – 3} \right) + k\pi
\end{array} \right.\left( {k \in Z} \right)\\
e){\sin ^2}x – 10\sin x\cos x + 21{\cos ^2}x = 0\\
\Leftrightarrow {\sin ^2}x – 3\sin x\cos x – 7\sin x\cos x + 21{\cos ^2}x = 0\\
\Leftrightarrow \left( {\sin x – 3\cos x} \right)\left( {\sin x – 7\cos x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin x = 3\cos x\\
\sin x = 7\cos x
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\tan x = 3\\
\tan x = 7
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \arctan 3 + k\pi \\
x = \arctan 7 + k\pi
\end{array} \right.\left( {k \in Z} \right)\\
f){\cos ^2}x – 3\sin x\cos x + 1 = 0\\
\Leftrightarrow {\cos ^2}x – 3\sin x\cos x + {\sin ^2}x + {\cos ^2}x = 0\\
\Leftrightarrow 2{\cos ^2}x – 3\sin x\cos x + {\sin ^2}x = 0\\
\Leftrightarrow \left( {\cos x – \sin x} \right)\left( {2\cos x – \sin x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = \sin x\\
2\cos x = \sin x
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\tan x = 1\\
\tan x = 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{4} + k\pi \\
x = \arctan 2 + k\pi
\end{array} \right.\left( {k \in Z} \right)
\end{array}$