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Category: Geometry

Question-64971

Question Number 64971 by Tawa1 last updated on 23/Jul/19 Commented by Tony Lin last updated on 23/Jul/19 x2sinθ=x2+1sin(90°+θ)=xsin(90°2θ)x2sinθ=x2+1cosθ=xcos2θletcosθ=t$$\Rightarrow\frac{\frac{{x}}{\mathrm{2}}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}=\frac{\frac{{x}}{\mathrm{2}}+\mathrm{1}}{{t}}=\frac{{x}}{\mathrm{2}{t}^{\mathrm{2}}…

Question-64887

Question Number 64887 by ajfour last updated on 22/Jul/19 Answered by mr W last updated on 22/Jul/19 letλ=aR$$\mathrm{cos}\:\alpha=\frac{\left(\frac{{a}}{\mathrm{2}}\right)^{\mathrm{2}} +{R}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}×\frac{{a}}{\mathrm{2}}×{R}}=\frac{\mathrm{4}{R}^{\mathrm{2}} −\mathrm{3}{a}^{\mathrm{2}} }{\mathrm{4}{aR}}=\frac{\mathrm{4}−\mathrm{3}\lambda^{\mathrm{2}}…