Question

What basic trigonometric identity would you use to verify that csc x sec x cot x = csc^(2)x

Answer 1

Answer:

Step-by-step explanation:

Using the basic trigonometry identity, we have

$cosecx=\frac{1}{sinx}$, $secx=\frac{1}{cosx}$ and $cotx=\frac{cosx}{sinx}$

Thus, the given equation is:

${\text}{cosecx secx cotx}=cosec^2x$

Taking the LHS of the above equation , we get

=${\text}{cosecx secx cotx}$

=$cosecx(\frac{1}{cosx})(\frac{cosx}{sinx})$

=$cosec^2x$

=RHS

Hence proved.

Answer 2

Answer:

 $cotx=\frac{cosx}{sinx}$

 $secx=\frac{1}{cosx}$

$cscx=\frac{1}{sinx}$

Step-by-step explanation:

1. Keeping on mind that $secx=\frac{1}{cosx}$ and  $cotx=\frac{cos}{sin}$, you can rewrite it as following:

$cscx(\frac{1}{cosx})(\frac{cosx}{sinx})$

2. Then, when you simplify it, you obtain:

$cscx\frac{1}{sinx}$

3. So, keeping on mind that $cscx=\frac{1}{sinx}$, you have:

$cscx*cscx=csc^{2}x$