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Question Number 207156 by hardmath last updated on 07/May/24
Find:   (1/(sin 10°)) − ((√3)/(cos 10°))  =  ?
$$\mathrm{Find}:\:\:\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}\:−\:\frac{\sqrt{\mathrm{3}}}{\mathrm{cos}\:\mathrm{10}°}\:\:=\:\:? \\ $$
Answered by A5T last updated on 07/May/24
=((2sin30)/(sin10))−((2cos30)/(cos10))=((2[sin30cos10−cos30sin10])/(sin10cos10))  =((2[sin(30−10)])/(sin10cos10))=((4sin20)/(2sin10cos10=sin20))=4
$$=\frac{\mathrm{2}{sin}\mathrm{30}}{{sin}\mathrm{10}}−\frac{\mathrm{2}{cos}\mathrm{30}}{{cos}\mathrm{10}}=\frac{\mathrm{2}\left[{sin}\mathrm{30}{cos}\mathrm{10}−{cos}\mathrm{30}{sin}\mathrm{10}\right]}{{sin}\mathrm{10}{cos}\mathrm{10}} \\ $$$$=\frac{\mathrm{2}\left[{sin}\left(\mathrm{30}−\mathrm{10}\right)\right]}{{sin}\mathrm{10}{cos}\mathrm{10}}=\frac{\mathrm{4}{sin}\mathrm{20}}{\mathrm{2}{sin}\mathrm{10}{cos}\mathrm{10}={sin}\mathrm{20}}=\mathrm{4} \\ $$

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