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Question Number 54156 by Tawa1 last updated on 30/Jan/19
Please sirs,  How is,      − cot(α)  =  tan((1/2)π + α)  ????
$$\mathrm{Please}\:\mathrm{sirs},\:\:\mathrm{How}\:\mathrm{is},\:\:\:\:\:\:−\:\mathrm{cot}\left(\alpha\right)\:\:=\:\:\mathrm{tan}\left(\frac{\mathrm{1}}{\mathrm{2}}\pi\:+\:\alpha\right)\:\:???? \\ $$
Commented by turbo msup by abdo last updated on 30/Jan/19
tan((π/2)+α) =((sin((π/2)+α))/(cos((π/2)+α)))  =((cosα)/(−sinα)) =−(1/(tanα)) =−cotanα .
$${tan}\left(\frac{\pi}{\mathrm{2}}+\alpha\right)\:=\frac{{sin}\left(\frac{\pi}{\mathrm{2}}+\alpha\right)}{{cos}\left(\frac{\pi}{\mathrm{2}}+\alpha\right)} \\ $$$$=\frac{{cos}\alpha}{−{sin}\alpha}\:=−\frac{\mathrm{1}}{{tan}\alpha}\:=−{cotan}\alpha\:. \\ $$

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