Question

Determinati x ∈ (0,$\frac{\pi }{2}$)

Stiind ca $\frac{3sin x + cos x}{sinx} = 4$

Answer 1

 

$\displaystyle\bf\\x\in\Big(0,~\frac{\pi}{2}\Big)\\\\sau\\\\x\in\Big(0,~90^o\Big)\\\\\\\frac{3sin\,x+cos\,x}{sin\,x}=4\\\\\\\frac{3sin\,x}{sin\,x}+\frac{cos\,x}{sin\,x}=4\\\\\\3+\frac{cos\,x}{sin\,x}=4\\\\\\\frac{cos\,x}{sin\,x}=4-3\\\\\\\frac{cos\,x}{sin\,x}=1\\\\\\ctg\,x=1\\\\\\x=arcctg(1)=\frac{\pi}{4}=45^o\\\\\\\boxed{\bf~x=\frac{\pi}{4}}\\\\ sau\\\\\boxed{\bf~x=45^o}$