Найдите при каких значениях аргумента значение функции равно двум объясните как решать подобные что такое аргумент?
Ответы на вопрос:
0\\\\\boxed {1+ctg^2a=\frac{1}{sin^2a}\; }\; \; \to \; \; \frac{1}{sin^2a}=1+(\sqrt2)^2=3\; \; \to \; \; sin^2a=\frac{1}{3}\\\\\\sina=\pm \frac{1}{\sqrt3}\\\\sina<0\; \; \Rightarrow \; \; sina=-\frac{1}{\sqrt3}=-\frac{\sqrt3}{3}\\\\tga=\dfrac{1}{ctga}=\dfrac{1}{\sqrt2}\\\\\\cosa=-\sqrt{1-sin^2a}=-\sqrt{1-\frac{1}{3}}=-\sqrt{\frac{2}{3}}=-\frac{\sqrt6}{3}" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=2%29%5C%3B%20%5C%3B%20ctga%3D%5Csqrt2%5C%5C%5C%5C%5Cpi%20%3Ca%3C%5Cfrac%7B3%5Cpi%7D%7B2%7D%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20sina%3C0%5C%3B%20%2C%5C%3B%20cosa%3C0%5C%3B%20%2C%5C%3B%20tga%3E0%5C%5C%5C%5C%5Cboxed%20%7B1%2Bctg%5E2a%3D%5Cfrac%7B1%7D%7Bsin%5E2a%7D%5C%3B%20%7D%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20%5Cfrac%7B1%7D%7Bsin%5E2a%7D%3D1%2B%28%5Csqrt2%29%5E2%3D3%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20sin%5E2a%3D%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%5C%5Csina%3D%5Cpm%20%5Cfrac%7B1%7D%7B%5Csqrt3%7D%5C%5C%5C%5Csina%3C0%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20sina%3D-%5Cfrac%7B1%7D%7B%5Csqrt3%7D%3D-%5Cfrac%7B%5Csqrt3%7D%7B3%7D%5C%5C%5C%5Ctga%3D%5Cdfrac%7B1%7D%7Bctga%7D%3D%5Cdfrac%7B1%7D%7B%5Csqrt2%7D%5C%5C%5C%5C%5C%5Ccosa%3D-%5Csqrt%7B1-sin%5E2a%7D%3D-%5Csqrt%7B1-%5Cfrac%7B1%7D%7B3%7D%7D%3D-%5Csqrt%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D-%5Cfrac%7B%5Csqrt6%7D%7B3%7D" title="2)\; \; ctga=\sqrt2\\\\\pi <a<\frac{3\pi}{2}\; \; \Rightarrow \; \; sina<0\; ,\; cosa<0\; ,\; tga>0\\\\\boxed {1+ctg^2a=\frac{1}{sin^2a}\; }\; \; \to \; \; \frac{1}{sin^2a}=1+(\sqrt2)^2=3\; \; \to \; \; sin^2a=\frac{1}{3}\\\\\\sina=\pm \frac{1}{\sqrt3}\\\\sina<0\; \; \Rightarrow \; \; sina=-\frac{1}{\sqrt3}=-\frac{\sqrt3}{3}\\\\tga=\dfrac{1}{ctga}=\dfrac{1}{\sqrt2}\\\\\\cosa=-\sqrt{1-sin^2a}=-\sqrt{1-\frac{1}{3}}=-\sqrt{\frac{2}{3}}=-\frac{\sqrt6}{3}">
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