Question

***Medal AND Fan Rewarded***
*** Attachment Below***
How do I verify the identity ?

Answer 1

If you use the trigonometric identities:\[1+\tan^2x = \sec^2x = \frac{ 1 }{ \cos^2x }\]\[\tan^2x = \frac{ \sin^2x }{ \cos^2x }\]
You can substitute them into the original equation and get:
\[\frac{( \frac{ 1 }{ \cos^2x }) }{ (\frac{ \sin^2x }{ \cos^2x }) }\] which can then be simplified to get sec^2x.

Answer 2

\[\sec^2x-\tan^2x=1 \therefore \sec^2x=1+\tan^2x\] substitute it in\[\frac{ sex^2x }{ \tan^2x }\] also written as \[\frac{ 1 }{ \cos^2x }\times \frac{ 1 }{ \tan^2x }\] which can also be written as \[\frac{ 1 }{\cos^2x }\times \frac{ \cos^2x }{ \sin^2x }\] do appropriate cancelling and you got your answer

Answer 3

Thanks for your help guys!!! :) Such a big help!!!

Answer 4

why does the x and the c have to be so close together

Answer 5

ummm idk???