double angle identities: sin2x=2sinxcosx=2sinxcosx/cosxsec^2x•cosxsec^2x

[ken_165]

double angle identities: sin2x=2sinxcosx=2sinxcosx/cosxsec^2x•cosxsec^2x

the equation says, sin2x=2sinxcosx=2sinxcosx/cosxsec^2x•cosxsec^2x. now, why is sec^2x is used?

 

[Deleted member 4993]

the equation says, sin2x=2sinxcosx=2sinxcosx/cosxsec^2x•cosxsec^2x. now, why is sec^2x is used?

We need to see the whole problem - that is, we need to know the "destination" to justify the path taken!

 

[Steven G]

the equation says, sin2x=2sinxcosx=2sinxcosx/cosxsec^2x•cosxsec^2x. now, why is sec^2x is used?

1st note that \(\displaystyle \frac{1}{sec^2x}*sec^2x =1\) So multiplying 2sinxcosx by 1 still gives you 2sinxcosx. It may look different but it is still equals 2sinxcosx. Now why did they do this? I have no idea as you did not give us the end result. Anytime you want to change the way that something looks you multiply it by one in a favorable way. Just tell us the end result and we will explain why that chose to multiply by \(\displaystyle \frac{1}{sec^2x}*sec^2x\)

 

[ken_165]

trigonometric identities

how about in this equation: cos2x=cos2x-sin2x... why is cos2x-sin2x is used?