How do you solve $4 cot x = cot x {sin}^{2} x$ $4cotx=cotxsin^2x$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?

Question

How do you solve $4 cot x = cot x {sin}^{2} x$ $4cotx=cotxsin^2x$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?

1 Answer

Related questions

How do you find all solutions trigonometric equations?
How do you express trigonometric expressions in simplest form?
How do you solve trigonometric equations by factoring?
How do you solve trigonometric equations by the quadratic formula?
How do you use the fundamental identities to solve trigonometric equations?
What are other methods for solving equations that can be adapted to solving trigonometric equations?
How do you solve ${sin}^{2} x - 2 sin x - 3 = 0$ $\sin^2 x - 2 \sin x - 3 = 0$ over the interval $[0, 2 π]$ $[0,2pi]$ ?
How do you find all the solutions for $2 {sin}^{2} \frac{x}{4} - 3 cos \frac{x}{4} = 0$ $2 \sin^2 \frac{x}{4}-3 \cos \frac{x}{4} = 0$ over the...
How do you solve ${cos}^{2} x = \frac{1}{16}$ $\cos^2 x = \frac{1}{16}$ over the interval $[0, 2 π]$ $[0,2pi]$ ?
How do you solve for x in $3 sin 2 x = cos 2 x$ $3sin2x=cos2x$ for the interval $0 ≤ x < 2π$

Impact of this question

6468 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-01T07:48:17

$x = \frac{π}{2}$ $x=pi/2$ and $x = \frac{3 π}{2}$ $x=(3pi)/2$

Explanation:

$4 cot x = cot x {sin}^{2} x$ $4cotx=cotxsin^2x$

$\Leftrightarrow cot x {sin}^{2} x - 4 cot x = 0$ $hArrcotxsin^2x-4cotx=0$

or $cot x ({sin}^{2} x - 4) = 0$ $cotx(sin^2x-4)=0$

As ${sin}^{2} x$ $sin^2x$ ranges from $0$ $0$ to $1$ $1$ , ${sin}^{2} x - 4 \neq 0$ $sin^2x-4!=0$

and hence we must have $cot x = 0$ $cotx=0$ .

Between $0$ $0$ and $2 π$ $2pi$ , $cot x = 0$ $cotx=0$ at $x = \frac{π}{2}$ $x=pi/2$ and $x = \frac{3 π}{2}$ $x=(3pi)/2$ and hence that is the solution,

Science

Math

Humanities

... and beyond

How do you solve $4 cot x = cot x {sin}^{2} x$ $4cotx=cotxsin^2x$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 4cotx=cotxsin^2x4cotx=cotxsin2x4cotx=cotxsin^2x for 0<=x<=2pi0≤x≤2π0<=x<=2pi?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $4 cot x = cot x {sin}^{2} x$ $4cotx=cotxsin^2x$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?