Verify that tan(2x) = 2sinxcosxsec(2x)

`tan(2x)=2sinxcosxsec2x`

To verify this identity, simplify the right side of the equation until it matches the left side.

(1) This verification will include the Double Angle formula:

 `sin(2x)=2sinxcosx`

(2) This verification will include the Reciprocal Identity:

`sec(x)=1/cos(x)`

(3) The verification will include the Quotient Identity:

`tan(x)=sin(x)/cos(x)`

Here are the steps.

`tan(2x)=2sin(x)cos(x)sec(2x)`

`tan(2x)=sin(2x)sec(2x)`    [Using the Double Angle Formula]

`tan(2x)=sin(2x)*1/cos(2x)`      [Using the Reciprocal Identity]

`tan(2x)=sin(2x)/cos(2x)`

`tan(2x)=tan(2x)`             ...

`tan(2x)=2sinxcosxsec2x`

To verify this identity, simplify the right side of the equation until it matches the left side.

(1) This verification will include the Double Angle formula:

 `sin(2x)=2sinxcosx`

(2) This verification will include the Reciprocal Identity:

`sec(x)=1/cos(x)`

(3) The verification will include the Quotient Identity:

`tan(x)=sin(x)/cos(x)`

Here are the steps.

`tan(2x)=2sin(x)cos(x)sec(2x)`

`tan(2x)=sin(2x)sec(2x)`    [Using the Double Angle Formula]

`tan(2x)=sin(2x)*1/cos(2x)`      [Using the Reciprocal Identity]

`tan(2x)=sin(2x)/cos(2x)`

`tan(2x)=tan(2x)`                  [Using the Quotient Identity]