Question Number 66768 by John Kaloki Musau last updated on 19/Aug/19
$${without}\:{using}\:{mathematical}\:{tables} \\ $$$${evaluate} \\ $$$$\frac{\mathrm{sin}\:\mathrm{60}.\mathrm{tan}\:\mathrm{30}.\mathrm{cos}\:\mathrm{60}+\mathrm{sin}\:\mathrm{30}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}}{\mathrm{sin}\:\mathrm{90}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}−\mathrm{sin}\:\mathrm{60}.\mathrm{cos}\:\mathrm{30}.\mathrm{sin}\:\mathrm{30}} \\ $$
Commented by Tony Lin last updated on 19/Aug/19
$$\frac{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}×\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}{\mathrm{1}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}}=\frac{\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{4}}}{\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{3}}{\mathrm{8}}}=\mathrm{4} \\ $$