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Category: Geometry

Question-154475

Question Number 154475 by mr W last updated on 18/Sep/21 Commented by mr W last updated on 18/Sep/21 $${find}\:{the}\:{area}\:{of}\:{the}\:{big}\:{triangle}\:{whose} \\ $$$${sides}\:{have}\:{the}\:{distances}\:\boldsymbol{{d}}_{\mathrm{1}} ,\boldsymbol{{d}}_{\mathrm{2}} ,\boldsymbol{{d}}_{\mathrm{3}} \:{to}\: \\…

Question-88865

Question Number 88865 by tw000001 last updated on 13/Apr/20 Commented by tw000001 last updated on 13/Apr/20 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{who}\:\mathrm{the}\:\mathrm{question}\:\mathrm{can}\:\mathrm{solve}. \\ $$ Terms of Service Privacy Policy Contact:…

sin-3-x-cos-x-dx-

Question Number 23317 by tapan das last updated on 28/Oct/17 $$\int\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx} \\ $$ Answered by mrW1 last updated on 28/Oct/17 $$=\int\mathrm{sin}^{\mathrm{3}} \:\mathrm{x}\:\mathrm{dsin}\:\mathrm{x} \\ $$$$=\frac{\mathrm{sin}^{\mathrm{4}}…

Question-154343

Question Number 154343 by Lekhraj last updated on 17/Sep/21 Answered by qaz last updated on 17/Sep/21 $$\frac{\mathrm{sin}\:\mathrm{x}}{\bullet\mathrm{O}}=\frac{\mathrm{sin}\:\angle\mathrm{M}\bullet\mathrm{C}}{\mathrm{OC}},\:\:\:\:\:\:\frac{\mathrm{sin}\:\mathrm{30}°}{\bullet\mathrm{O}}=\frac{\mathrm{sin}\:\mathrm{105}°}{\mathrm{OA}} \\ $$$$\because\:\:\mathrm{OA}=\mathrm{OC}\:\:\:\:\:\: \\ $$$$\therefore\:\:\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{sin}\:\mathrm{30}°}{\mathrm{sin}\:\mathrm{105}°}\centerdot\mathrm{sin}\:\angle\mathrm{M}\bullet\mathrm{C}=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\mathrm{sin}\:\angle\mathrm{M}\bullet\mathrm{C} \\ $$$$\because\:\:\:\angle\mathrm{M}\bullet\mathrm{C}=\mathrm{180}°−\mathrm{135}°−\mathrm{x}=\mathrm{45}°−\mathrm{x} \\ $$$$\therefore\:\:\:\mathrm{sin}\:\mathrm{x}=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\mathrm{sin}\:\left(\mathrm{45}°−\mathrm{x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\left(\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}\right)…