Answer: OPTION B.
Step-by-step explanation:
It is important to remember these identities:
[tex]csc(x)=\frac{1}{sin(x)}\\\\sec(x)=\frac{1}{cos(x)}[/tex]
Knowing this, we can say that:
[tex]csc(x) sec(x)=\frac{1}{sin(x)}*\frac{1}{cos(x)}=\frac{1}{sin(x)*cos(x)}[/tex]
Now we need to use the following Double angle identity :
[tex]sin(2x)=2sin(x)cos(x)[/tex]
And solve for [tex]sin(x)cos(x)[/tex]:
[tex]\frac{sin(2x)}{2}=sin(x)cos(x)[/tex]
The next step is to make the substitution into [tex]\frac{1}{sin(x)*cos(x)}[/tex] and finally simplify:
[tex]\frac{1}{\frac{sin(2x)}{2}}=\frac{\frac{1}{1}}{\frac{sin(2x)}{2}}=\frac{2}{sin(2x)}=2csc(2x)[/tex]
