Question

Daca X apartine ( 0, pi supra 2 ) si cos X =5 SUPRA 13 ,ARATA-TI ca tg x =12 supra 5 .

Answer 1

$\displaystyle x\in\left(0,\frac\pi2\right)\Rightarrow \sin x>0\text{ \c si }\cos x>0\\\sin^2x+\cos^2x=1\\\sin^2x=1-\cos^2x=\displaystyle 1-\frac{25}{169}=\frac{144}{169}\\\displaystyle\sin x=\pm\frac{12}{13}\\\text{Cum }\sin x>0\Rightarrow\sin x=\displaystyle\frac{12}{13}\\\displaystyle tg x=\frac{\sin x}{\cos x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}$