Sina*cosa = 0.5*sin(2a)
sina + cosa = 4/3 - возведем обе части уравнения в квадрат
(sin^2(a) + 2sina*cosa + cos^2(a)) = 16/9
sin(2a) + 1 = 16/9
sin(2a) = (16/9) - 1 = 7/9
sina*cosa = 0.5*(7/9) = 7/18
7х если там везде умножить
Sin x = 0,21; cos x = √(1 - sin^2 x) = √(1 - 0,0441) = √(0,9559)
![sin(x/2)= \sqrt{ \frac{1-cos(x)}{2} } = \sqrt{ \frac{1- \sqrt{0,9559} }{2} }](https://tex.z-dn.net/?f=sin%28x%2F2%29%3D+%5Csqrt%7B+%5Cfrac%7B1-cos%28x%29%7D%7B2%7D+%7D+%3D+%5Csqrt%7B+%5Cfrac%7B1-+%5Csqrt%7B0%2C9559%7D+%7D%7B2%7D+%7D+)
![cos(x/2)= \sqrt{ \frac{1+cos(x)}{2} } = \sqrt{ \frac{1+ \sqrt{0,9559} }{2} }](https://tex.z-dn.net/?f=cos%28x%2F2%29%3D+%5Csqrt%7B+%5Cfrac%7B1%2Bcos%28x%29%7D%7B2%7D+%7D+%3D+%5Csqrt%7B+%5Cfrac%7B1%2B+%5Csqrt%7B0%2C9559%7D+%7D%7B2%7D+%7D+)
![sin(x/2)+cos(x/2)=\sqrt{ \frac{1- \sqrt{0,9559} }{2} }+\sqrt{ \frac{1+ \sqrt{0,9559} }{2} }](https://tex.z-dn.net/?f=sin%28x%2F2%29%2Bcos%28x%2F2%29%3D%5Csqrt%7B+%5Cfrac%7B1-+%5Csqrt%7B0%2C9559%7D+%7D%7B2%7D+%7D%2B%5Csqrt%7B+%5Cfrac%7B1%2B+%5Csqrt%7B0%2C9559%7D+%7D%7B2%7D+%7D)
≈ 0,1056 + 0,9944 = 1,1
1/(2x+5)=1/(6x-5)
2x+5=6x-5
2x-6x=-5-5
-4x=-10
x=10/4
x=2.5
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