Question

daca x apartine ( 0 , π:2 ) si cosx= radical din 2 : 2
aratati ca tg x=1

Answer 1

[tex]\it x \in (0, \dfrac{\pi}{2}) \\\;\\ cosx=\dfrac{\sqrt2}{2} \Longrightarrow x = \dfrac{\pi}{4} \\\;\\ \\\;\\ tg\dfrac{\pi}{4} = 1[/tex]

Answer 2

[tex]x \ apartine \ [0, \frac{ \pi} {2} ] \\ sin^{2}x+ cos^{2}x= 1 \rightarrow sin x = \sqrt{1-cos^{2}x} = \sqrt{1-( \frac{ \sqrt{2} }{2} )^{2}} = \sqrt{1- \frac{2}{4} } = \\ \sqrt{ \frac{2}{4}} = \frac{ \sqrt{2}} {2 } \\ \\ \\ tg x= \frac{sinx}{cosx}= \frac{ \frac{ \sqrt{2}} {2}} {\frac{ \sqrt{2} }{2}} =1[/tex]