Question

Solve tan(x){tan(%) - 1) = 0 O A. x = 5 + 27T7,X = 3 37 + 27 O B. x = -2779,x=37 + X +277, X = +27 2. C. X = +19,X = = tnx +277 O D. X = n,X = x FT 4

Answer 1

Given the trigonometry equation below,

$\tan (x)(\tan (x)-1)=0$

Solving each part separately

$\begin{gathered} \tan \mleft(x\mright)=0\quad \mathrm{or}\quad \tan \mleft(x\mright)-1=0 \\ x=\tan ^{-1}0\text{ or tan(x)=1} \\ x=\pm n\pi\text{ }or\text{ }x=tan^{-1}1 \\ x=\pm n\pi\text{ or x=45} \\ x=\pm n\pi\text{ or x=}\frac{\pi}{45}\pm n\pi \end{gathered}$

Therefore,

$x=\pm n\pi,\text{ x=}\frac{\pi}{45}\pm n\pi$

Hence, Option D is the correct answer.