Question

Use basic trigonometric identities to simplify the expression: 2 sin (x) cos (x) sec (x) csc (x) = ?

Answer 1

Answer:

$2sin(x)*cos(x)*sec(x)*csc (x)=2$

Step-by-step explanation:

Remember the identities:

$sec(x)=\frac{1}{cos(x)}\\\\csc(x)=\frac{1}{sin(x)}$

Ginven the expression:

$2sin(x)*cos(x)*sec(x)*csc (x)$

You need to substitute $sec(x)=\frac{1}{cos(x)}$ and $csc(x)=\frac{1}{sin(x)}$ into it:

$2sin(x)*cos(x)*sec(x)*csc (x)=2sin(x)*cos(x)*\frac{1}{cos(x)}*\frac{1}{sin(x)}$

Now, you need to simplify.

Remember that:

$\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}$

And:

$\frac{a}{a}=1$

Then, you get:

$=\frac{2sin(x)*cos(x)}{cos(x)*sin(x)}}=2$