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




Question Number 207330 by hardmath last updated on 11/May/24
Find:   4 cos 50°  +  (1/(sin 20°))  =  ?
$$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{cos}\:\mathrm{50}°\:\:+\:\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{20}°}\:\:=\:\:? \\ $$
Answered by som(math1967) last updated on 12/May/24
 ((4sin20cos50+1)/(sin20))  =((2(sin70−sin30)+1)/(sin20))  =((2sin70−1+1)/(cos(90−20)))  =2tan70=5.49
$$\:\frac{\mathrm{4}{sin}\mathrm{20}{cos}\mathrm{50}+\mathrm{1}}{{sin}\mathrm{20}} \\ $$$$=\frac{\mathrm{2}\left({sin}\mathrm{70}−{sin}\mathrm{30}\right)+\mathrm{1}}{{sin}\mathrm{20}} \\ $$$$=\frac{\mathrm{2}{sin}\mathrm{70}−\mathrm{1}+\mathrm{1}}{{cos}\left(\mathrm{90}−\mathrm{20}\right)} \\ $$$$=\mathrm{2}{tan}\mathrm{70}=\mathrm{5}.\mathrm{49} \\ $$

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