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cos65-m-sin40-




Question Number 11258 by uni last updated on 18/Mar/17
cos65=m  ⇒ sin40=?
$${cos}\mathrm{65}={m}\:\:\Rightarrow\:{sin}\mathrm{40}=? \\ $$
Answered by ajfour last updated on 18/Mar/17
let p=sin 40 =cos 50    p =sin 40= 1−2sin^2 25  sin 25 = cos 65 =m  so, sin 40 =1−2m^2  .
$$\mathrm{let}\:\mathrm{p}=\mathrm{sin}\:\mathrm{40}\:=\mathrm{cos}\:\mathrm{50} \\ $$$$\:\:\mathrm{p}\:=\mathrm{sin}\:\mathrm{40}=\:\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{25} \\ $$$$\mathrm{sin}\:\mathrm{25}\:=\:\mathrm{cos}\:\mathrm{65}\:=\mathrm{m} \\ $$$$\mathrm{so},\:\mathrm{sin}\:\mathrm{40}\:=\mathrm{1}−\mathrm{2m}^{\mathrm{2}} \:. \\ $$

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