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Используем формулу:
![sin^2a - sin^2b = sin(a+b)sin(a-b)\ \2sin(frac{pi}{4}+x)sin(frac{pi}{4}-x)+sin^2x=0\2sin^2frac{pi}{4}-2sin^2x+sin^2x=0\2*(frac{sqrt2}{2})^2-sin^2x=0\1-sin^2x=0\sinx=pm1\\1)sinx=1\x=frac{pi}{2}+2pi n, ; nin Z;\\2)sinx=-1\x=-frac{pi}{2}+2pi k, ; kin Z.\](https://tex.z-dn.net/?f=sin%5E2a+-+sin%5E2b+%3D+sin%28a%2Bb%29sin%28a-b%29%5C+%5C2sin%28frac%7Bpi%7D%7B4%7D%2Bx%29sin%28frac%7Bpi%7D%7B4%7D-x%29%2Bsin%5E2x%3D0%5C2sin%5E2frac%7Bpi%7D%7B4%7D-2sin%5E2x%2Bsin%5E2x%3D0%5C2%2A%28frac%7Bsqrt2%7D%7B2%7D%29%5E2-sin%5E2x%3D0%5C1-sin%5E2x%3D0%5Csinx%3Dpm1%5C%5C1%29sinx%3D1%5Cx%3Dfrac%7Bpi%7D%7B2%7D%2B2pi+n%2C+%3B+nin+Z%3B%5C%5C2%29sinx%3D-1%5Cx%3D-frac%7Bpi%7D%7B2%7D%2B2pi+k%2C+%3B+kin+Z.%5C "sin^2a - sin^2b = sin(a+b)sin(a-b)\ \2sin(frac{pi}{4}+x)sin(frac{pi}{4}-x)+sin^2x=0\2sin^2frac{pi}{4}-2sin^2x+sin^2x=0\2*(frac{sqrt2}{2})^2-sin^2x=0\1-sin^2x=0\sinx=pm1\\1)sinx=1\x=frac{pi}{2}+2pi n, ; nin Z;\\2)sinx=-1\x=-frac{pi}{2}+2pi k, ; kin Z.\")
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