0\\t^2+2t-3=0\\D=4+4\cdot3=16\\t_1=1,\\t_2=-3\;-\;He\;nogx.\\\left(\frac23\right)^{\cos x}=1\Rightarrow\cos x=0\\x=\frac\pi2+\pi n,\;n\in\mathbb{Z}" alt="\left(\frac49\right)^{\cos x}+2\cdot\left(\frac23\right)^{\cos x}-3=0\\\left(\frac23\right)^{2\cos x}+2\cdot\left(\frac23\right)^{\cos x}-3=0\\\left(\frac23\right)^{\cos x}=t,\;\left(\frac23\right)^{2\cos x}=t^2,\;t>0\\t^2+2t-3=0\\D=4+4\cdot3=16\\t_1=1,\\t_2=-3\;-\;He\;nogx.\\\left(\frac23\right)^{\cos x}=1\Rightarrow\cos x=0\\x=\frac\pi2+\pi n,\;n\in\mathbb{Z}" align="absmiddle" class="latex-formula">
![b)\;x\in[\pi;\;4\pi]\\\pi\geq\frac\pi2+\pi n\geq4\pi\\\frac\pi2\geq\pi n\geq\frac{7\pi}2\\\frac12\geq n\geq\frac72\\n\in\mathbb{Z}\Rightarrow n\in[1;3]\\n=1\Rightarrow x=\frac\pi2+\pi=\frac{3\pi}2\\n=2\Rightarrow x=\frac\pi2+2\pi=\frac{5\pi}2\\n=3\Rightarrow x=\frac\pi2+3\pi=\frac{7\pi}2](https://tex.z-dn.net/?f=b%29%5C%3Bx%5Cin%5B%5Cpi%3B%5C%3B4%5Cpi%5D%5C%5C%5Cpi%5Cgeq%5Cfrac%5Cpi2%2B%5Cpi+n%5Cgeq4%5Cpi%5C%5C%5Cfrac%5Cpi2%5Cgeq%5Cpi+n%5Cgeq%5Cfrac%7B7%5Cpi%7D2%5C%5C%5Cfrac12%5Cgeq+n%5Cgeq%5Cfrac72%5C%5Cn%5Cin%5Cmathbb%7BZ%7D%5CRightarrow+n%5Cin%5B1%3B3%5D%5C%5Cn%3D1%5CRightarrow+x%3D%5Cfrac%5Cpi2%2B%5Cpi%3D%5Cfrac%7B3%5Cpi%7D2%5C%5Cn%3D2%5CRightarrow+x%3D%5Cfrac%5Cpi2%2B2%5Cpi%3D%5Cfrac%7B5%5Cpi%7D2%5C%5Cn%3D3%5CRightarrow+x%3D%5Cfrac%5Cpi2%2B3%5Cpi%3D%5Cfrac%7B7%5Cpi%7D2 "b)\;x\in[\pi;\;4\pi]\\\pi\geq\frac\pi2+\pi n\geq4\pi\\\frac\pi2\geq\pi n\geq\frac{7\pi}2\\\frac12\geq n\geq\frac72\\n\in\mathbb{Z}\Rightarrow n\in[1;3]\\n=1\Rightarrow x=\frac\pi2+\pi=\frac{3\pi}2\\n=2\Rightarrow x=\frac\pi2+2\pi=\frac{5\pi}2\\n=3\Rightarrow x=\frac\pi2+3\pi=\frac{7\pi}2")