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+(1)/(sinx)=0`

Simplify

`\begin{gathered} 6s\imaginaryI nx+(1)/(s\imaginaryI nx)=0 \\ \\ (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=-(1)/(6) \end{gathered}`

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

No Solution