Saturday, December 12, 2015

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]




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