Làm dùm em câu d , câu e cậu f vs ạ

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Làm dùm em câu d , câu e cậu f vs ạ
lam-dum-em-cau-d-cau-e-cau-f-vs-a

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Huy Gia 4 years 2020-10-28T22:41:28+00:00 1 Answers 83 views 0

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  1. Bo
    0
    2020-10-28T22:42:58+00:00
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    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}$

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