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Уравнение имеет четыре корня.
![(frac{1}{cos^2x}-1)sqrt{25-x^2}=0\ ; ; ODZ:; 25-x^2 geq 0,; ; x^2-25 leq 0,; ; (x-5)(x+5) leq 0\xin [-5,5]\a); frac{1}{cos^2x}-1=tg^2x=0,; to tgx=0,; x=pi n,; nin Z\pi nin [-5,5]; to; x_1=-pi ,; x_2=pi \b); sqrt{25-x^2}=0,; 25-x^2=0; to ; x_3=-5,; x_4=5](https://tex.z-dn.net/?f=%28frac%7B1%7D%7Bcos%5E2x%7D-1%29sqrt%7B25-x%5E2%7D%3D0%5C+%3B+%3B+ODZ%3A%3B+25-x%5E2+geq+0%2C%3B+%3B+x%5E2-25+leq+0%2C%3B+%3B+%28x-5%29%28x%2B5%29+leq+0%5Cxin+%5B-5%2C5%5D%5Ca%29%3B+frac%7B1%7D%7Bcos%5E2x%7D-1%3Dtg%5E2x%3D0%2C%3B+to+tgx%3D0%2C%3B+x%3Dpi+n%2C%3B+nin+Z%5Cpi+nin+%5B-5%2C5%5D%3B+to%3B+x_1%3D-pi+%2C%3B+x_2%3Dpi++%5Cb%29%3B+sqrt%7B25-x%5E2%7D%3D0%2C%3B+25-x%5E2%3D0%3B+to+%3B+x_3%3D-5%2C%3B+x_4%3D5 "(frac{1}{cos^2x}-1)sqrt{25-x^2}=0\ ; ; ODZ:; 25-x^2 geq 0,; ; x^2-25 leq 0,; ; (x-5)(x+5) leq 0\xin [-5,5]\a); frac{1}{cos^2x}-1=tg^2x=0,; to tgx=0,; x=pi n,; nin Z\pi nin [-5,5]; to; x_1=-pi ,; x_2=pi \b); sqrt{25-x^2}=0,; 25-x^2=0; to ; x_3=-5,; x_4=5")
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