Question

Ştiind că ctg x = 3 , să se calculeze ctg 2x .

Answer 1

Salut,

$ctg(2x)=\dfrac{1}{tg(2x)}=\dfrac{1}{\dfrac{2tgx}{1-tg^2x}}=\dfrac{1-tg^2x}{2tgx}=\dfrac{1-\dfrac{1}{ctg^2x}}{2\dfrac{1}{ctgx}}=\dfrac{ctg^2x-1}{ctg^2x}\cdot\dfrac{ctgx}{2}=\\\\\\=\dfrac{ctg^2x-1}{2ctgx}=\dfrac{3^2-1}{2\cdot 3}=\dfrac{8}6=\dfrac{4}3.$

Învață formulele de la trigonometrie !

Green eyes.