Question

Which of the following are solutions to the equation sinx cosx = S? Check all that apply. . 13. 51 12 . c.플 EN D. + 12

Answer 1

`x=(\pi)/(12)+n\pi.\text{ Option D is correct.}`

Explanations:

Given the trigonometry equation expressed as;

`sinxcosx=(1)/(4)`

We are to simplify for the value(s) of 'x"

Recall from trigonometry identity that:

`\begin{gathered} Sin2x=2sinxcosx \\ sinxcosx=(sin2x)/(2) \end{gathered}`

Substitute the result into the original equation to have:

`\begin{gathered} (sin2x)/(2)=(1)/(4) \\ sin2x=(1)/(2) \end{gathered}`

Solve for the value of "x"

`\begin{gathered} 2x=sin^(-1)((1)/(2)) \\ 2x=30^0 \\ x=(30)/(2) \\ x=15 \\ x=(\pi)/(12) \\ \end{gathered}`

The general solution to the given trigonometry function is:

`x=(\pi)/(12)+n\pi`