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Câu 18 trang 29 SGK Đại số và Giải tích 11 Nâng cao

Giải các phương trình sau :
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Lựa chọn câu để xem lời giải nhanh hơn
Giải các phương trình sau:

LG a

\(\tan 3x = \tan {{3\pi } \over 5}\)

Lời giải chi tiết:

\(\tan 3x = \tan {{3\pi } \over 5} \Leftrightarrow 3x = {{3\pi } \over 5} + k\pi \) \(\Leftrightarrow x = {\pi \over 5} + k{\pi \over 3},k \in\mathbb Z\)

LG b

\(\tan(x – 15^0) = 5\)

Lời giải chi tiết:

\(\begin{array}{l}
\tan \left( {x - {{15}^0}} \right) = 5\\
\Leftrightarrow x - {15^0} = \arctan 5 + k{180^0}\\
\Leftrightarrow x = {15^0} + \arctan 5 + k{180^0},k \in\mathbb Z
\end{array}\)

Cách trình bày khác:

\(\tan(x – 15^0) = 5\) \(⇔ x = α + 15^0+ k180^0\), trong đó \(\tan α = 5\) (chẳng hạn, có thể chọn \(α ≈ 78^041’24”\) nhờ dùng máy tính bỏ túi)

LG c

\(\tan \left( {2x - 1} \right) = \sqrt 3 \)

Lời giải chi tiết:

\(\eqalign{
& \tan \left( {2x - 1} \right) = \sqrt 3 \cr&\Leftrightarrow \tan \left( {2x - 1} \right) = \tan {\pi \over 3} \cr 
💙& \Leftrightarrow 2x - 1 = {\pi \over 3} + k\pi \cr&\Leftrightarrow x = {\pi \over 6} + {1 \over 2} + k{\pi \over 2};k \in\mathbb Z \cr} \)

LG d

\(\cot 2x = \cot \left( { - {1 \over 3}} \right)\)

Lời giải chi tiết:

\(\cot 2x = \cot \left( { - {1 \over 3}} \right) \) \(\Leftrightarrow 2x = - {1 \over 3} + k\pi \) \(\Leftrightarrow x = - {1 \over 6} + k{\pi \over 2},k \in\mathbb Z\)

LG e

\(\cot \left( {{x \over 4} + 20^\circ } \right) = - \sqrt 3 \)

Lời giải chi tiết:

\(\eqalign{
& \cot \left( {{x \over 4} + 20^\circ } \right) = - \sqrt 3\cr& \Leftrightarrow \cot \left( {{x \over 4} + 20^\circ } \right) = \cot \left( { - 30^\circ } \right) \cr 
🔜& \Leftrightarrow {x \over 4} + 20^\circ = - 30^\circ + k180^\circ \cr&\Leftrightarrow x = - 200^\circ + k720^\circ ,k \in\mathbb Z \cr} \)

LG f

\(\cot 3x = \tan {{2\pi } \over 5}\)

Lời giải chi tiết:

\(\cot 3x = \tan {{2\pi } \over 5}\) \(\Leftrightarrow \cot 3x = \cot \left( {{\pi \over 2} - {{2\pi } \over 5}} \right)\)\( = \cot \frac{\pi }{{10}}\) \(\Leftrightarrow 3x = {\pi \over {10}} + k\pi \) \(\Leftrightarrow x = {\pi \over {30}} + k.{\pi \over 3},k \in\mathbb Z \)

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