Question

Solve for x for 0 ≤ x < 2 π .

cotxcosx - cotx = 0


0

Pi/2

Pi

3Pi/2

2Pi

Answer 1

`\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} (\pi )/(2)\\\\ (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}`

Answer 2

x = π/2, 3π/2

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