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Find-4-sin-50-1-cos-20-




Question Number 207328 by hardmath last updated on 11/May/24
Find:   4 sin 50° − (1/(cos 20°))  =  ?
$$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{sin}\:\mathrm{50}°\:−\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{20}°}\:\:=\:\:? \\ $$
Answered by som(math1967) last updated on 12/May/24
 ((4sin50cos20−1)/(cos20))  =((2(sin70+sin30)−1)/(sin(90−20)))  =((2sin70+1−1)/(sin70))=2
$$\:\frac{\mathrm{4}{sin}\mathrm{50}{cos}\mathrm{20}−\mathrm{1}}{{cos}\mathrm{20}} \\ $$$$=\frac{\mathrm{2}\left({sin}\mathrm{70}+{sin}\mathrm{30}\right)−\mathrm{1}}{{sin}\left(\mathrm{90}−\mathrm{20}\right)} \\ $$$$=\frac{\mathrm{2}{sin}\mathrm{70}+\mathrm{1}−\mathrm{1}}{{sin}\mathrm{70}}=\mathrm{2} \\ $$

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