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




Question Number 146242 by mathdanisur last updated on 12/Jul/21
4 sin(50°) - (1/(cos(20°))) = ?
$$\mathrm{4}\:{sin}\left(\mathrm{50}°\right)\:-\:\frac{\mathrm{1}}{{cos}\left(\mathrm{20}°\right)}\:=\:? \\ $$
Answered by gsk2684 last updated on 12/Jul/21
=((4cos 40^0 cos 20^0 −1)/(cos 20^0 ))  =((2(cos 60^0 +cos 20^0 )−1)/(cos 20^0 ))  =((2((1/2)+cos 20^0 )−1)/(cos 20^0 ))  =2
$$=\frac{\mathrm{4cos}\:\mathrm{40}^{\mathrm{0}} \mathrm{cos}\:\mathrm{20}^{\mathrm{0}} −\mathrm{1}}{\mathrm{cos}\:\mathrm{20}^{\mathrm{0}} } \\ $$$$=\frac{\mathrm{2}\left(\mathrm{cos}\:\mathrm{60}^{\mathrm{0}} +\mathrm{cos}\:\mathrm{20}^{\mathrm{0}} \right)−\mathrm{1}}{\mathrm{cos}\:\mathrm{20}^{\mathrm{0}} } \\ $$$$=\frac{\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\mathrm{20}^{\mathrm{0}} \right)−\mathrm{1}}{\mathrm{cos}\:\mathrm{20}^{\mathrm{0}} } \\ $$$$=\mathrm{2} \\ $$
Commented by mathdanisur last updated on 12/Jul/21
thankyou Ser
$${thankyou}\:{Ser} \\ $$

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