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tan193-k-cos167-




Question Number 188725 by 073 last updated on 06/Mar/23
tan193=k  cos167=?
$$\mathrm{tan193}=\mathrm{k} \\ $$$$\mathrm{cos167}=? \\ $$
Answered by BaliramKumar last updated on 06/Mar/23
tan193 = k  tan(180+13)= tan13 = k  cos167 = cos(180−13) = −cos13  −cos13 = ((−1)/(sec13)) = ((−1)/( (√(1+tan^2 13)))) = ((−1)/( (√(1+k^2 ))))
$${tan}\mathrm{193}\:=\:{k} \\ $$$${tan}\left(\mathrm{180}+\mathrm{13}\right)=\:{tan}\mathrm{13}\:=\:{k} \\ $$$${cos}\mathrm{167}\:=\:{cos}\left(\mathrm{180}−\mathrm{13}\right)\:=\:−{cos}\mathrm{13} \\ $$$$−{cos}\mathrm{13}\:=\:\frac{−\mathrm{1}}{{sec}\mathrm{13}}\:=\:\frac{−\mathrm{1}}{\:\sqrt{\mathrm{1}+{tan}^{\mathrm{2}} \mathrm{13}}}\:=\:\frac{−\mathrm{1}}{\:\sqrt{\mathrm{1}+{k}^{\mathrm{2}} }} \\ $$
Commented by 073 last updated on 06/Mar/23
nice solution
$$\mathrm{nice}\:\mathrm{solution} \\ $$

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