[tex]\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}[/tex]
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
