Toán Lớp 11: Giải phương trình: cos(2x + 150°)+3sin(15° – x) – 1=0
Giúp mk với ạ
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 11: Giải phương trình: cos(2x + 150°)+3sin(15° – x) – 1=0
Giúp mk với ạ
Comments ( 1 )
\quad \cos(2x + 150^\circ) + 3\sin(15^\circ – x) – 1 =0\\
\Leftrightarrow \cos[180^\circ + 2(x – 15^\circ)] + 3\sin(15^\circ – x) – 1 =0\\
\Leftrightarrow – \cos[2(x – 15^\circ)] + 3\sin(15^\circ – x) – 1 =0\\
\Leftrightarrow -\cos[2(15^\circ-x)] + 3\sin(15^\circ – x) – 1 =0\\
\Leftrightarrow – [1 – 2\sin^2(15^\circ – x)] + 3\sin(15^\circ – x) – 1 =0\\
\Leftrightarrow 2\sin^2(15^\circ – x)+ 3\sin(15^\circ – x) – 2 =0\\
\Leftrightarrow [2\sin(15^\circ – x) -1][\sin(15^\circ – x) + 2] = 0\\
\Leftrightarrow \left[\begin{array}{l}\sin(15^\circ – x) = \dfrac12\\\sin(15^\circ – x) = 2\quad (vn)\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}15^\circ – x = 30^\circ + k.180^\circ\\15^\circ – x = 150^\circ + k.180^\circ\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = -15^\circ + k.180^\circ\\x = -135^\circ + k.180^\circ\end{array}\right.\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{-15^\circ + k.180^\circ;\ -135^\circ + k.180^\circ\ \Big|\ k\in\Bbb Z\right\}
\end{array}\)