Помогите, пожалуйста!особенно с первым примером

Question 1

Question 2

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Question 3

   $m*sin(x+15)=n*sin(x-75)\\ sin(90-(75-x))=cos(75-x)=cos(-(x-75))=cos(x-75)\\ m*cos(x-75)=n*sin(x-75)\\ m*cos(x-75)-n*sin(x-75)=0\\ x-75+165-x=0\\\\ m=cos(165-x)\\ n=sin(165-x)$
так как $m,n \in N\\ 165-x=90\\ x=75$
$m=0\\ n=1\\ x=75$


0\\ x^{ log_{2}x*0.5} > 0\\ x\in(-\infty;+\infty)\\\\ x^{0.5*log_{2}x} \geq 4\\ x^{log_{2}x} \geq 16\\ log_{2}x*log_{2}x \geq 4\\ log^2_{2}x \geq 4\\ x\in(0;\frac{1}{4}]\cup [4; \infty) " alt="\sqrt{x^{log_{2}\sqrt{x}}} \geq 2\\ \sqrt{x^{\frac{log_{2}x}{2}}} \geq 2\\ x>0\\ x^{ log_{2}x*0.5} > 0\\ x\in(-\infty;+\infty)\\\\ x^{0.5*log_{2}x} \geq 4\\ x^{log_{2}x} \geq 16\\ log_{2}x*log_{2}x \geq 4\\ log^2_{2}x \geq 4\\ x\in(0;\frac{1}{4}]\cup [4; \infty) " align="absmiddle" class="latex-formula">

Матов_zn · Answer 1 · 2018-03-18T21:21:55+0000

   $m*sin(x+15)=n*sin(x-75)\\ sin(90-(75-x))=cos(75-x)=cos(-(x-75))=cos(x-75)\\ m*cos(x-75)=n*sin(x-75)\\ m*cos(x-75)-n*sin(x-75)=0\\ x-75+165-x=0\\\\ m=cos(165-x)\\ n=sin(165-x)$
так как $m,n \in N\\ 165-x=90\\ x=75$
$m=0\\ n=1\\ x=75$


0\\ x^{ log_{2}x*0.5} > 0\\ x\in(-\infty;+\infty)\\\\ x^{0.5*log_{2}x} \geq 4\\ x^{log_{2}x} \geq 16\\ log_{2}x*log_{2}x \geq 4\\ log^2_{2}x \geq 4\\ x\in(0;\frac{1}{4}]\cup [4; \infty) " alt="\sqrt{x^{log_{2}\sqrt{x}}} \geq 2\\ \sqrt{x^{\frac{log_{2}x}{2}}} \geq 2\\ x>0\\ x^{ log_{2}x*0.5} > 0\\ x\in(-\infty;+\infty)\\\\ x^{0.5*log_{2}x} \geq 4\\ x^{log_{2}x} \geq 16\\ log_{2}x*log_{2}x \geq 4\\ log^2_{2}x \geq 4\\ x\in(0;\frac{1}{4}]\cup [4; \infty) " align="absmiddle" class="latex-formula">