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Compare-sin-43-and-sin-40-sin-3-




Question Number 145668 by mathdanisur last updated on 07/Jul/21
Compare:  sin(43°)  and  sin(40°)+sin(3°)
$${Compare}: \\ $$$${sin}\left(\mathrm{43}°\right)\:\:{and}\:\:{sin}\left(\mathrm{40}°\right)+{sin}\left(\mathrm{3}°\right) \\ $$
Answered by mr W last updated on 07/Jul/21
sin 43°=sin (40+3)  =cos 3×sin 40+cos 40×sin 3  <sin 40°+sin 3°
$$\mathrm{sin}\:\mathrm{43}°=\mathrm{sin}\:\left(\mathrm{40}+\mathrm{3}\right) \\ $$$$=\mathrm{cos}\:\mathrm{3}×\mathrm{sin}\:\mathrm{40}+\mathrm{cos}\:\mathrm{40}×\mathrm{sin}\:\mathrm{3} \\ $$$$<\mathrm{sin}\:\mathrm{40}°+\mathrm{sin}\:\mathrm{3}° \\ $$
Commented by mathdanisur last updated on 07/Jul/21
Thankyou Ser
$${Thankyou}\:{Ser} \\ $$

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