Answer:
d. 0, 1.369
Step-by-step explanation:
Given:
The equation is: [tex]\tan x =5\sin x................(0\leq x\leq \pi)[/tex]
Adding [tex]-5\sin x[/tex] on both sides, we get
[tex]\tan x - 5\sin x=0[/tex]
Using the identity [tex]\tan x=\frac{\sin x}{\cos x}[/tex], we get
[tex]\frac{\sin x}{\cos x}-5\sin x=0[/tex]
Factoring out [tex]\sin x[/tex], we get
[tex]\sin x(\frac{1}{\cos x}-5)=0\\\\\therefore \sin x=0\ or\ \frac{1}{\cos x}-5=0\\\\x=\sin^{-1} (0)\ or\ \cos x=\frac{1}{5}\\\\x=0\ or\ x=\cos^{-1} (\frac{1}{5})\\\\x=0\ or\ x=1.3694\approx 1.369(\textrm{Round to 3 decimal places})[/tex]
Therefore, the solution of the given equation is either 0 or 1.369.
The correct choice is d.
