(x+6)ˇ2 -(x-5)(x+5)=79
xˇ2+12x+36-xˇ2+25=79
12x+61=79
12x=18, x=3/2
5*(x2+6x+9). Наверное так
Область допустимых значений уравнения : tgx≠0, х≠πn, n∈Z и х≠π/2+πk, k∈Z
![\frac{cos3x}{ \frac{sinx}{cosx} } =sin3x-2sinx, \\ cosx\cdot cos3x=sinx\cdot sin3x-2sin^{2}x, \\ cos3x\cdot cosx-sin3x\cdot sinx=-2sin^{2}x, \\ cos(3x+x)=-2sin^{2}x, \\ cos4x+2sin^{2}x=0, \\ (2cos ^{2} 2x-1)+(1-cos2x)=0, \\ 2cos ^{2} 2x-cos2x=0, \\ cos2x\cdot (2cos2x-1)=0 ](https://tex.z-dn.net/?f=+%5Cfrac%7Bcos3x%7D%7B+%5Cfrac%7Bsinx%7D%7Bcosx%7D+%7D+%3Dsin3x-2sinx%2C+%5C%5C++cosx%5Ccdot+cos3x%3Dsinx%5Ccdot+sin3x-2sin%5E%7B2%7Dx%2C+%5C%5C+cos3x%5Ccdot+cosx-sin3x%5Ccdot+sinx%3D-2sin%5E%7B2%7Dx%2C+%5C%5C+cos%283x%2Bx%29%3D-2sin%5E%7B2%7Dx%2C+%5C%5C++cos4x%2B2sin%5E%7B2%7Dx%3D0%2C+%5C%5C+%282cos+%5E%7B2%7D+2x-1%29%2B%281-cos2x%29%3D0%2C+%5C%5C+2cos+%5E%7B2%7D+2x-cos2x%3D0%2C+%5C%5C+cos2x%5Ccdot+%282cos2x-1%29%3D0%0A)
Произведение равно нулю, когда хотя один из множителей равен нулю, а другой при этом не теряет смысла.
![\left \{ {{cos2x=0} \atop {2cos2x-1=0}} \right. \Rightarrow \left \{ {{cos2x=0} \atop {cos2x= \frac{1}{2} }}\Rightarrow \left \{ {{2x= \frac{ \pi }{2} + \pi k,k\in Z} \atop {2x=\pm \frac{ \pi }{3}+2 \pi n,n\in Z }} \right. \right. \Rightarrow \left \{ {{x= \frac{ \pi }{4} + \frac{ \pi }{2}k,k\in Z } \atop {x=\pm \frac{ \pi }{6}= \pi n,n\in Z }} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bcos2x%3D0%7D+%5Catop+%7B2cos2x-1%3D0%7D%7D+%5Cright.+%5CRightarrow+%5Cleft+%5C%7B+%7B%7Bcos2x%3D0%7D+%5Catop+%7Bcos2x%3D+%5Cfrac%7B1%7D%7B2%7D+%7D%7D%5CRightarrow+%5Cleft+%5C%7B+%7B%7B2x%3D+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B+%5Cpi+k%2Ck%5Cin+Z%7D+%5Catop+%7B2x%3D%5Cpm+%5Cfrac%7B+%5Cpi+%7D%7B3%7D%2B2+%5Cpi+n%2Cn%5Cin+Z+%7D%7D+%5Cright.++%5Cright.+%5CRightarrow+%5Cleft+%5C%7B+%7B%7Bx%3D+%5Cfrac%7B+%5Cpi+%7D%7B4%7D+%2B+%5Cfrac%7B+%5Cpi+%7D%7B2%7Dk%2Ck%5Cin+Z+%7D+%5Catop+%7Bx%3D%5Cpm++%5Cfrac%7B+%5Cpi+%7D%7B6%7D%3D+%5Cpi+n%2Cn%5Cin+Z+%7D%7D+%5Cright.+)
Ответ.
![\frac{ \pi }{4}+ \frac{ \pi }{2} k, \pm \frac{ \pi }{6} + \pi n,k,n\in Z](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+k%2C++%5Cpm+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%2B+%5Cpi+n%2Ck%2Cn%5Cin+Z+)