-1+(-a+√a)a/√a+√a
-1+-a²+a√a/2√a
-a²-1+a√a/2√a
-√aa²-√a*1+√aa√a/2*a
-a²√a-√a+√a√a/2a
-a²√a-√a+aa/2a
a²-a²√a-√a/2a
Ответ:
Объяснение:
1км^2=1*10^10 см ^2
1м^2=1*10^4 см ^2
35,9*10^12 cм^2=35.9*10^8 м^2 (12-4)
35,9*10^12 cм^2=35,9*10^2 км^2 (12-10)
![\cos (7x) -\cos x - \sin (4x)=0\\\\-2\cdot \sin\dfrac{7x+x}2\cdot \sin \dfrac{7x-x}2-\sin(4x)=0\\\\-2\cdot \sin(4x)\cdot \sin (3x)-\sin(4x)=0~~~~|\cdot (-1)\\2\cdot \sin(4x)\cdot \sin (3x)+\sin(4x)=0\\\sin(4x)\Big(2\sin (3x)+1\Big)=0](https://tex.z-dn.net/?f=%5Ccos+%287x%29+-%5Ccos+x+-+%5Csin+%284x%29%3D0%5C%5C%5C%5C-2%5Ccdot+%5Csin%5Cdfrac%7B7x%2Bx%7D2%5Ccdot+%5Csin+%5Cdfrac%7B7x-x%7D2-%5Csin%284x%29%3D0%5C%5C%5C%5C-2%5Ccdot+%5Csin%284x%29%5Ccdot+%5Csin+%283x%29-%5Csin%284x%29%3D0~~~~%7C%5Ccdot+%28-1%29%5C%5C2%5Ccdot+%5Csin%284x%29%5Ccdot+%5Csin+%283x%29%2B%5Csin%284x%29%3D0%5C%5C%5Csin%284x%29%5CBig%282%5Csin+%283x%29%2B1%5CBig%29%3D0)
![1) ~~\sin(4x)=0;\\~~~~~4x=\pi n,~~x_1=\dfrac{\pi n}4,~~n \in Z\\\\2) ~~2\sin(3x)+1=0;~~\sin (3x)=-\dfrac12\\\\~~~~\left[\begin{array}{c}3x=-\dfrac{\pi }6+2\pi k;~~x_2=-\dfrac{\pi}{18}+\dfrac{2\pi k}3,~~k \in Z\\\\3x=-\dfrac{5\pi }6+2\pi m;~~x_3=-\dfrac{5\pi}{18}+\dfrac{2\pi m}3,~~m \in Z\end{array}](https://tex.z-dn.net/?f=1%29+~~%5Csin%284x%29%3D0%3B%5C%5C~~~~~4x%3D%5Cpi+n%2C~~x_1%3D%5Cdfrac%7B%5Cpi+n%7D4%2C~~n+%5Cin+Z%5C%5C%5C%5C2%29+~~2%5Csin%283x%29%2B1%3D0%3B~~%5Csin+%283x%29%3D-%5Cdfrac12%5C%5C%5C%5C~~~~%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3x%3D-%5Cdfrac%7B%5Cpi+%7D6%2B2%5Cpi+k%3B~~x_2%3D-%5Cdfrac%7B%5Cpi%7D%7B18%7D%2B%5Cdfrac%7B2%5Cpi+k%7D3%2C~~k+%5Cin+Z%5C%5C%5C%5C3x%3D-%5Cdfrac%7B5%5Cpi+%7D6%2B2%5Cpi+m%3B~~x_3%3D-%5Cdfrac%7B5%5Cpi%7D%7B18%7D%2B%5Cdfrac%7B2%5Cpi+m%7D3%2C~~m+%5Cin+Z%5Cend%7Barray%7D)
Ответ: ![\dfrac{\pi n}4;~~~~-\dfrac{\pi}{18}+\dfrac{2\pi k}3;~~~~-\dfrac{5\pi}{18}+\dfrac{2\pi m}3,~~n,k,m \in Z](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpi+n%7D4%3B~~~~-%5Cdfrac%7B%5Cpi%7D%7B18%7D%2B%5Cdfrac%7B2%5Cpi+k%7D3%3B~~~~-%5Cdfrac%7B5%5Cpi%7D%7B18%7D%2B%5Cdfrac%7B2%5Cpi+m%7D3%2C~~n%2Ck%2Cm+%5Cin+Z)
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![\sin^2x+6\cos^2x+7\sin x \cos x=0~~~~|:\cos x \neq 0~\\\\ \dfrac{\sin^2x}{\cos^2x}+6+\dfrac{7\sin x\cos x}{\cos^2 x}=0\\\\ tg^2x+7~tgx + 6 = 0\\(tgx+6)(tgx+1)=0\\\\1)~tg x = -6; ~~x_1=-arctg~6+\pi n,~~n\in Z\\\\2)~tgx=-1;~~x_2=-\dfrac{\pi}4+\pi k,~~k \in Z](https://tex.z-dn.net/?f=%5Csin%5E2x%2B6%5Ccos%5E2x%2B7%5Csin+x+%5Ccos+x%3D0~~~~%7C%3A%5Ccos+x+%5Cneq+0~%5C%5C%5C%5C+%5Cdfrac%7B%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%2B6%2B%5Cdfrac%7B7%5Csin+x%5Ccos+x%7D%7B%5Ccos%5E2+x%7D%3D0%5C%5C%5C%5C+tg%5E2x%2B7~tgx+%2B+6+%3D+0%5C%5C%28tgx%2B6%29%28tgx%2B1%29%3D0%5C%5C%5C%5C1%29~tg+x+%3D+-6%3B+~~x_1%3D-arctg~6%2B%5Cpi+n%2C~~n%5Cin+Z%5C%5C%5C%5C2%29~tgx%3D-1%3B~~x_2%3D-%5Cdfrac%7B%5Cpi%7D4%2B%5Cpi+k%2C~~k+%5Cin+Z)
Ответ: ![-arctg~6+\pi n;~~~-\dfrac{\pi}4+\pi k,~~n,k \in Z](https://tex.z-dn.net/?f=-arctg~6%2B%5Cpi+n%3B~~~-%5Cdfrac%7B%5Cpi%7D4%2B%5Cpi+k%2C~~n%2Ck+%5Cin+Z)
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![4\sin^2x+5\sin x\cos x-\cos^2x=2\\4\sin^2x+5\sin x\cos x-\cos^2x-2(\sin^2x+\cos^2x)=0\\4\sin^2x+5\sin x\cos x-\cos^2x-2\sin^2x-2\cos^2x=0\\2\sin^2x+5\sin x\cos x-3\cos^2x=0~~~~|:\cos^2x\neq 0\\\\\dfrac{2\sin^2x}{\cos^2x}+\dfrac{5\sin x\cos x}{\cos^2x}-\dfrac{3\cos^2x}{\cos^2x}=0\\\\2tg^2x+5tgx-3=0\\D=25-4\cdot 2\cdot (-3)=49=7^2\\\\1)~tgx=\dfrac{-5+7}4=\dfrac12;~~x_1=arctg\dfrac12+\pi n,~n \in Z\\\\2)~tgx=\dfrac{-5-7}4=-3;~~x_2=-arctg3+\pi k,~k \in Z](https://tex.z-dn.net/?f=4%5Csin%5E2x%2B5%5Csin+x%5Ccos+x-%5Ccos%5E2x%3D2%5C%5C4%5Csin%5E2x%2B5%5Csin+x%5Ccos+x-%5Ccos%5E2x-2%28%5Csin%5E2x%2B%5Ccos%5E2x%29%3D0%5C%5C4%5Csin%5E2x%2B5%5Csin+x%5Ccos+x-%5Ccos%5E2x-2%5Csin%5E2x-2%5Ccos%5E2x%3D0%5C%5C2%5Csin%5E2x%2B5%5Csin+x%5Ccos+x-3%5Ccos%5E2x%3D0~~~~%7C%3A%5Ccos%5E2x%5Cneq+0%5C%5C%5C%5C%5Cdfrac%7B2%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%2B%5Cdfrac%7B5%5Csin+x%5Ccos+x%7D%7B%5Ccos%5E2x%7D-%5Cdfrac%7B3%5Ccos%5E2x%7D%7B%5Ccos%5E2x%7D%3D0%5C%5C%5C%5C2tg%5E2x%2B5tgx-3%3D0%5C%5CD%3D25-4%5Ccdot+2%5Ccdot+%28-3%29%3D49%3D7%5E2%5C%5C%5C%5C1%29~tgx%3D%5Cdfrac%7B-5%2B7%7D4%3D%5Cdfrac12%3B~~x_1%3Darctg%5Cdfrac12%2B%5Cpi+n%2C~n+%5Cin+Z%5C%5C%5C%5C2%29~tgx%3D%5Cdfrac%7B-5-7%7D4%3D-3%3B~~x_2%3D-arctg3%2B%5Cpi+k%2C~k+%5Cin+Z)
Ответ: ![arctg\dfrac12+\pi n;~~~-arctg3+\pi k,~n,k \in Z](https://tex.z-dn.net/?f=arctg%5Cdfrac12%2B%5Cpi+n%3B~~~-arctg3%2B%5Cpi+k%2C~n%2Ck+%5Cin+Z)
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![\sin (2x) + \sqrt 2\sin \Big(x-\dfrac{\pi}4\Big)=1\\\\ 2\sin x\cos x + \sqrt 2\Big(\sin x\cos \dfrac{\pi}4-\sin\dfrac{\pi}4\cos x\Big)=1\\\\ 2\sin x\cos x + \sqrt 2\Big(\dfrac{\sqrt2}2\sin x-\dfrac{\sqrt2}2\cos x\Big)=1\\\\ 2\sin x\cos x + \sin x-\cos x-1=0\\2\sin x\cos x + \sin x-\cos x-\sin^2-\cos^2x=0~~~|\cdot (-1)\\ \cos^2x-2\sin x\cos x + \sin^2x+\cos x-\sin x=0\\(\cos x- \sin x)^2+(\cos x-\sin x)=0\\(\cos x- \sin x)(\cos x-\sin x+1)=0](https://tex.z-dn.net/?f=%5Csin+%282x%29+%2B+%5Csqrt+2%5Csin+%5CBig%28x-%5Cdfrac%7B%5Cpi%7D4%5CBig%29%3D1%5C%5C%5C%5C+2%5Csin+x%5Ccos+x+%2B+%5Csqrt+2%5CBig%28%5Csin+x%5Ccos+%5Cdfrac%7B%5Cpi%7D4-%5Csin%5Cdfrac%7B%5Cpi%7D4%5Ccos+x%5CBig%29%3D1%5C%5C%5C%5C+2%5Csin+x%5Ccos+x+%2B+%5Csqrt+2%5CBig%28%5Cdfrac%7B%5Csqrt2%7D2%5Csin+x-%5Cdfrac%7B%5Csqrt2%7D2%5Ccos+x%5CBig%29%3D1%5C%5C%5C%5C+2%5Csin+x%5Ccos+x+%2B+%5Csin+x-%5Ccos+x-1%3D0%5C%5C2%5Csin+x%5Ccos+x+%2B+%5Csin+x-%5Ccos+x-%5Csin%5E2-%5Ccos%5E2x%3D0~~~%7C%5Ccdot+%28-1%29%5C%5C+%5Ccos%5E2x-2%5Csin+x%5Ccos+x+%2B+%5Csin%5E2x%2B%5Ccos+x-%5Csin+x%3D0%5C%5C%28%5Ccos+x-+%5Csin+x%29%5E2%2B%28%5Ccos+x-%5Csin+x%29%3D0%5C%5C%28%5Ccos+x-+%5Csin+x%29%28%5Ccos+x-%5Csin+x%2B1%29%3D0)
![1)~\cos x-\sin x=0;~~\cos x=\sin x\\\\~~~x_1=\dfrac{\pi}4+\pi n,~n \in Z\\\\2)~\cos x-\sin x+1=0;~~(1+\cos x)-\sin x=0\\\\~~~~2\cos^2\dfrac x2-2\sin \dfrac x2\cos \dfrac x2=0\\\\ ~~~~2\cos \dfrac x2\Big(\cos \dfrac x2-\sin \dfrac x2\Big)=0\\\\~~~~a) \cos \dfrac x2=0;~~\dfrac x2=\dfrac {\pi}2+\pi k;~~x_2=\pi + 2\pi k,~k \in Z\\\\~~~~b)\cos \dfrac x2-\sin \dfrac x2=0;~~\cos \dfrac x2=\sin \dfrac x2\\\\~~~~\dfrac x2=\dfrac {\pi}4+ \pi m; ~~x_3=\dfrac{\pi}2+2\pi m, ~m \in Z](https://tex.z-dn.net/?f=1%29~%5Ccos+x-%5Csin+x%3D0%3B~~%5Ccos+x%3D%5Csin+x%5C%5C%5C%5C~~~x_1%3D%5Cdfrac%7B%5Cpi%7D4%2B%5Cpi+n%2C~n+%5Cin+Z%5C%5C%5C%5C2%29~%5Ccos+x-%5Csin+x%2B1%3D0%3B~~%281%2B%5Ccos+x%29-%5Csin+x%3D0%5C%5C%5C%5C~~~~2%5Ccos%5E2%5Cdfrac+x2-2%5Csin+%5Cdfrac+x2%5Ccos+%5Cdfrac+x2%3D0%5C%5C%5C%5C+~~~~2%5Ccos+%5Cdfrac+x2%5CBig%28%5Ccos+%5Cdfrac+x2-%5Csin+%5Cdfrac+x2%5CBig%29%3D0%5C%5C%5C%5C~~~~a%29+%5Ccos+%5Cdfrac+x2%3D0%3B~~%5Cdfrac+x2%3D%5Cdfrac+%7B%5Cpi%7D2%2B%5Cpi+k%3B~~x_2%3D%5Cpi+%2B+2%5Cpi+k%2C~k+%5Cin+Z%5C%5C%5C%5C~~~~b%29%5Ccos+%5Cdfrac+x2-%5Csin+%5Cdfrac+x2%3D0%3B~~%5Ccos+%5Cdfrac+x2%3D%5Csin+%5Cdfrac+x2%5C%5C%5C%5C~~~~%5Cdfrac+x2%3D%5Cdfrac+%7B%5Cpi%7D4%2B+%5Cpi+m%3B+~~x_3%3D%5Cdfrac%7B%5Cpi%7D2%2B2%5Cpi+m%2C+~m+%5Cin+Z)
Ответ: ![\dfrac{\pi}4+\pi n;~~\pi + 2\pi k;~~\dfrac{\pi}2+2\pi m, ~~n,k,m \in Z](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpi%7D4%2B%5Cpi+n%3B~~%5Cpi+%2B+2%5Cpi+k%3B~~%5Cdfrac%7B%5Cpi%7D2%2B2%5Cpi+m%2C+~~n%2Ck%2Cm+%5Cin+Z)