Question Number 155628 by amin96 last updated on 03/Oct/21
Answered by mr W last updated on 03/Oct/21
$${BM}={MC}=\mathrm{1} \\ $$$${AC}=\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\frac{\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{45}+{x}\right)\:\mathrm{sin}\:\mathrm{30}}=\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{sin}\:\left(\mathrm{30}+{x}\right)} \\ $$$$\frac{\mathrm{1}}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}=\frac{\mathrm{2}}{\mathrm{cos}\:{x}+\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}} \\ $$$$\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)\mathrm{sin}\:{x}=\mathrm{cos}\:{x} \\ $$$$\mathrm{tan}\:{x}=\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{3}}}=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$$\Rightarrow{x}=\mathrm{15}° \\ $$
Commented by Tawa11 last updated on 03/Oct/21
$$\mathrm{Great}\:\mathrm{sir} \\ $$