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Question Number 66768 by John Kaloki Musau last updated on 19/Aug/19

without using mathematical tables  evaluate  ((sin 60.tan 30.cos 60+sin 30.cos 45.sin 45)/(sin 90.cos 45.sin 45−sin 60.cos 30.sin 30))

$${without}\:{using}\:{mathematical}\:{tables} \\ $$$${evaluate} \\ $$$$\frac{\mathrm{sin}\:\mathrm{60}.\mathrm{tan}\:\mathrm{30}.\mathrm{cos}\:\mathrm{60}+\mathrm{sin}\:\mathrm{30}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}}{\mathrm{sin}\:\mathrm{90}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}−\mathrm{sin}\:\mathrm{60}.\mathrm{cos}\:\mathrm{30}.\mathrm{sin}\:\mathrm{30}} \\ $$

Commented by Tony Lin last updated on 19/Aug/19

((((√3)/2)×(1/(√3))×(1/2)+(1/2)×((√2)/2)×((√2)/2))/(1×((√2)/2)×((√2)/2)−((√3)/2)×((√3)/2)×(1/2)))=(((1/4)+(1/4))/((1/2)−(3/8)))=4

$$\frac{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}×\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}{\mathrm{1}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}}=\frac{\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{4}}}{\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{3}}{\mathrm{8}}}=\mathrm{4} \\ $$

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