Question

Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)6 sin x + csc x = 0

Answer 1

we have the equation

$6sinx+cscx=0$

Rewrite the equation

$6s\imaginaryI nx+\frac{1}{sinx}=0$

Simplify

$\begin{gathered} 6s\imaginaryI nx+\frac{1}{s\imaginaryI nx}=0 \\ \\ \frac{6sin^2x+1}{sinx}=0 \end{gathered}$

Remember that

The denominator cannot be equal to zero

so

The value of angle x cannot be equal to x=0 and x=2pi

Solve the numerator

$\begin{gathered} 6sin^2x=-1 \\ sin^2x=-\frac{1}{6} \end{gathered}$

The equation has no solution because the function sine squared cannot be a negative number

No Solution