Question

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

Answer 1

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

Explanation:

Remember the identities:

`sec(x)=(1)/(cos(x))\\\\csc(x)=(1)/(sin(x))`

Ginven the expression:

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

You need to substitute
`sec(x)=(1)/(cos(x))` and
`csc(x)=(1)/(sin(x))` into it:

`2sin(x)*cos(x)*sec(x)*csc (x)=2sin(x)*cos(x)*(1)/(cos(x))*(1)/(sin(x))`

Now, you need to simplify.

Remember that:

`(a)/(b)*(c)/(d)=(a*c)/(b*d)`

And:

`(a)/(a)=1`

Then, you get:

`=(2sin(x)*cos(x))/(cos(x)*sin(x))}=2`