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Category: Trigonometry

Question-100491

Question Number 100491 by bobhans last updated on 27/Jun/20 Answered by bramlex last updated on 27/Jun/20 $${let}\:\mathrm{arccot}\:\frac{\mathrm{1}}{\mathrm{2}}\:=\:{z}\:\Rightarrow\:\mathrm{cot}\:{z}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${let}\:\mathrm{arccot}\:\frac{\mathrm{2}}{\mathrm{3}}\:=\:{w}\:\Rightarrow\mathrm{cot}\:{w}\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\Leftrightarrow\mathrm{tan}\:\left({z}+{w}\right)\:=\:\frac{\mathrm{tan}\:{z}+\mathrm{tan}\:{w}}{\mathrm{1}−\mathrm{tan}\:{z}.\mathrm{tan}\:{w}} \\ $$$$=\:\frac{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{2}}}{\mathrm{1}−\mathrm{2}.\frac{\mathrm{3}}{\mathrm{2}}}\:=\:\frac{\mathrm{7}}{\mathrm{2}−\mathrm{6}}\:=\:−\frac{\mathrm{7}}{\mathrm{4}\:}\:\blacksquare\: \\ $$…

sinx-siny-3-2-2-sin-x-2-sin-y-2-2-faind-x-

Question Number 165995 by mathlove last updated on 11/Feb/22 $$\begin{cases}{{sinx}+{siny}=\frac{\mathrm{3}}{\mathrm{2}}}\\{\mathrm{2}^{\mathrm{sin}\:{x}} +\mathrm{2}^{\mathrm{sin}\:{y}} =\mathrm{2}+\sqrt{\mathrm{2}}}\end{cases}\:\:\:\:\:\:\:{faind}\:\:\:{x}=? \\ $$ Answered by alephzero last updated on 11/Feb/22 $$\begin{cases}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{y}\:=\:\frac{\mathrm{3}}{\mathrm{2}}}\\{\mathrm{2}^{\mathrm{sin}\:{x}} +\:\mathrm{2}^{\mathrm{cos}\:{y}} \:=\:\mathrm{2}\:+\:\sqrt{\mathrm{2}}}\end{cases} \\…