Giúp mình với, bí rồi :( Cách làm tương tự nhau mà kết quả khác là sao ạ?
Giải phương trình sau:
cos5x=sin3xCách 1:
cos5x=sin3x⇔cos5x=cos(π2−3x)$\Leftrightarrow \left[\begin{gathered}5x=\frac{\pi }{2}-3x+k2\pi
\\ 5x=-\frac{\pi }{2}+3x+k2\pi
\\ \end{gathered}\right.$$\Leftrightarrow \left[\begin{gathered}8x=\frac{\pi }{2}+k2\pi
\\ 2x=-\frac{\pi }{2}+k2\pi
\\ \end{gathered}\right.
\Leftrightarrow \left[\begin{gathered}x=\frac{\pi }{16}+k\frac{\pi }{4} \\ x=-\frac{\pi }{4}+k\pi \\ \end{gathered}\right.$Cách 2: $\cos 5x=\sin 3x\Leftrightarrow \sin 3x=\sin \left ( \frac{\pi }{2}-5x \right )
\Leftrightarrow \left[\begin{gathered}3x=\frac{\pi }{2}-5x+k2\pi \\ 3x=\pi -\frac{\pi }{2}+5x+k2\pi \\ \end{gathered}\right.\Leftrightarrow \left[
\begin{gathered}3x+5x= \frac{\pi }{2}+k2\pi \\ 3x-5x=\pi -\frac{\pi }{2}+k2\pi \\ \end{gathered}\right.
\Leftrightarrow \left[\begin{gathered}8x=\frac{\pi }{2}+k2\pi \\ -2x=\frac{\pi }{2}+k2\pi \\ \end{gathered}\right.\Leftrightarrow \left[\begin{gathered}x=\frac{\pi }{16}+k\frac{\pi }{4}\\ x=-\frac{\pi }{4}-k\pi
\\ \end{gathered}\right.$
Giúp mình với, bí rồi :( Cách làm tương tự nhau mà kết quả khác là sao ạ?
Giải phương trình sau:
\cos 5x=\sin 3xCách 1:
\cos 5x=\sin 3x\Leftrightarrow \cos 5x=\cos \left ( \frac{\pi }{2}-3x \right )\Leftrightarrow \left[\begin{gathered}5x=\frac{\pi }{2}-3x+k2\pi \\ 5x=-\frac{\pi }{2}+3x+k2\pi \\ \end{gathered}\right.\Leftrightarrow \left[\begin{gathered}8x=\frac{\pi }{2}+k2\pi \\ 2x=-\frac{\pi }{2}+k2\pi \\ \end{gathered}\right.\Leftrightarrow \left[\begin{gathered}x=\frac{\pi }{16}+k\frac{\pi }{4} \\ x=-\frac{\pi }{4}+k\pi \\ \end{gathered}\right.Cách 2:
\cos 5x=\sin 3x\Leftrightarrow \sin 3x=\sin \left ( \frac{\pi }{2}-5x \right )\Leftrightarrow \left[\begin{gathered}3x=\frac{\pi }{2}-5x+k2\pi \\ 3x=\pi -\frac{\pi }{2}+5x+k2\pi \\ \end{gathered}\right.\Leftrightarrow \left[\begin{gathered}3x+5x= \frac{\pi }{2}+k2\pi \\ 3x-5x=\pi -\frac{\pi }{2}+k2\pi \\ \end{gathered}\right.\Leftrightarrow \left[\begin{gathered}8x=\frac{\pi }{2}+k2\pi \\ -2x=\frac{\pi }{2}+k2\pi \\ \end{gathered}\right.\Leftrightarrow \left[\begin{gathered}x=\frac{\pi }{16}+k\frac{\pi }{4}\\ x=-\frac{\pi }{4}-k\pi \\ \end{gathered}\right.