Question

Solve for x for 0 ≤ x < 2 π .

Answer 1

Answer:

x = π/2, 3π/2  

Step-by-step explanation:

cot(x)cos(x) - cot(x) = 0

Factor out cot(x)

cot(x)[cos(x) -1] = 0

Solve each part separately

cot(x) = 0                cos(x) - 1 = 0

x = π/2, 3π/2           cos(x) = 1

                                x = 0

There are three possible solutions:

x = 0, π/2, 3π/2

However, the function is undefined for x = 0.

∴ x = π/2, 3π/2

Answer 2

$\bf cot(x)cos(x)-cot(x)=0\implies cot(x)[cos(x)-1]=0 \\\\[-0.35em] ~\dotfill\\\\ cot(x)=0\implies \cfrac{cos(x)}{sin(x)}=0\implies cos(x)=0\\\\\\ x=cos^{-1}(0)\implies \boxed{x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ cos(x)-1=0\implies cos(x)=1\implies x=cos^{-1}(1)\implies \boxed{x=0}$