Question

Which of the following identities can you use to help vou show that tan (3x)=sin(6x)/1+cos(6x)Select all that apply 3 answers

Answer 1

Given

`\tan3x=(\sin6x)/(1+\cos6x)`

Find

Find which identities used to show

`\tan3x=(\sin6x)/(1+\cos6x)`

Step-by-step explanation

as,, we use

`\begin{gathered} \sin2x=2\sin x\cos x \\ \cos2x=2\cos^2x-1 \end{gathered}`

so ,

`\begin{gathered} \sin(6x)=2\sin(3x)\cos(3x) \\ \cos(6x)=2\cos^2(3x)-1 \end{gathered}`

now, substitute the values on the left side

`\begin{gathered} (2\sin(3x)\cos(3x))/(1+(2\cos^2(3x)-1)) \\ \\ \frac{\begin{equation*}2\sin(3x)\cos(3x)\end{equation*}}{1+2\cos^2(3x)-1} \\ \\ (2\sin(3x)\cos(3x))/(2\cos^2(3x)) \\ \\ (\sin(3x))/(\cos(3x)) \\ \\ \tan(3x) \end{gathered}`

Final Answer

Therefore . we use 3 identities which are A , B and D