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starting with cos^2(x)+sin^2(x)=1 and using your knownledge of the quotient and reciprocal identities. derive an equivlaent identity in terms of tan(x) and sec(x)

 Mar 31, 2015

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 #1
avatar+128083 
+5

 cos^2(x)+sin^2(x)=1    divide everything by cos^2x

1 + sin^x /cos^x  = 1/cos^2x

1 + tan'2x  = sec^2x

So

sec^2x - tan'2x  = 1  =  sin^2x + cos^2x

And these identites are equivalent..... {I assume that's what you wanted }

 

  

 Mar 31, 2015
 #1
avatar+128083 
+5
Best Answer

 cos^2(x)+sin^2(x)=1    divide everything by cos^2x

1 + sin^x /cos^x  = 1/cos^2x

1 + tan'2x  = sec^2x

So

sec^2x - tan'2x  = 1  =  sin^2x + cos^2x

And these identites are equivalent..... {I assume that's what you wanted }

 

  

CPhill Mar 31, 2015

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