Giải phương trình sin(2x + 30°) = sin 60°.

29/38

Giải phương trình \(\sin \left( {2x + {{30}^0}} \right) = \sin {60^0}\).

\(\left[ \begin{array}{l}x = {15^0} + k{180^0}\\x = {45^0} + k{180^0}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right).\)

\(\left[ \begin{array}{l}x = {15^0} + k{360^0}\\x = {45^0} + k{260^0}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right).\)

\(\left[ \begin{array}{l}x = {60^0} + k{180^0}\\x = {90^0} + k{180^0}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right).\)

\(\left[ \begin{array}{l}x = {60^0} + k{360^0}\\x = {90^0} + k{360^0}\end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right).\)

Giải thích

Chọn A

Ta có \[\sin \left( {2x + {{30}^0}} \right) = \sin {60^0} \Leftrightarrow \left[ \begin{array}{l}2x + {30^0} = {60^0} + k{360^0}\\2x + {30^0} = {180^0} - {60^0} + k{360^0}\end{array} \right.\left( {k \in \mathbb{Z}} \right) \Leftrightarrow \left[ \begin{array}{l}x = {15^0} + k{180^0}\\x = {45^0} + k{180^0}\end{array} \right.\left( {k \in \mathbb{Z}} \right)\]