Q:

"Verify the identity of (sinx cosx)^2/sinx cosx = 2 + secx cscx"this is for a friend and she's needing help big time

Accepted Solution

A:

(sinx + cosx)^2/((sinx)(cosx)) = 2 + (secx)(cscx) 
(sinx + cosx)^2/((sinx)(cosx)) = 2 + 1/(sinxcosx); subtract 1/sinxcosx both sides 
(sinx + cosx)^2/((sinx)(cosx)) - 1/(sinxcosx)= 2; multiply through by sinxcosx 
(sinx + cosx)^2 -1 = 2(sinxcosx) 
sin^2 + 2sinxcosx + cos^2 - 1 = 2(sinxcosx); since sin^x + cos^2x = 1 
1 + 2sinxcosx -1 = 2sinxcosx 
2sinxcosx = 2sinxcosx