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Category: Trigonometry

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} \\…

If-3sin-x-4cos-x-5-then-sin-x-

Question Number 100131 by bemath last updated on 25/Jun/20 $$\mathrm{If}\:\mathrm{3sin}\:\mathrm{x}+\mathrm{4cos}\:\mathrm{x}=\mathrm{5}\:\mathrm{then}\:\mathrm{sin}\:\mathrm{x}=? \\ $$ Commented by bobhans last updated on 25/Jun/20 $$\mathrm{let}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:=\:\mathrm{t}\:,\:\Rightarrow\mathrm{sin}\:\mathrm{x}\:=\:\frac{\mathrm{2t}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\:,\:\mathrm{cos}\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{t}^{\mathrm{2}} }{\mathrm{1}+\mathrm{t}^{\mathrm{2}} } \\ $$$$\Leftrightarrow\frac{\mathrm{6t}+\mathrm{4}−\mathrm{4t}^{\mathrm{2}}…

how-many-integer-number-satisfy-the-equation-sin-x-x-2-x-2-4x-5-0-

Question Number 100130 by bemath last updated on 25/Jun/20 $$\mathrm{how}\:\mathrm{many}\:\mathrm{integer}\:\mathrm{number}\: \\ $$$$\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\frac{\mathrm{sin}\:\mathrm{x}−\mid\mathrm{x}+\mathrm{2}\mid}{\mathrm{x}^{\mathrm{2}} −\mathrm{4x}−\mathrm{5}}\:\geqslant\:\mathrm{0}\: \\ $$ Answered by mr W last updated on 25/Jun/20…