SOLUTION: I need help verifying these identities. {{{Sin(x)Cos(x)+Cos^2x = Cos(x)(1+Cot(x))/Csc(x)}}} AND {{{(Sec(x)-Tan(x))^2 + (Sec(x)+Tan(x))^2 = 2+4Tan^2x}}}

Question 168554: I need help verifying these identities.

AND

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
): I need help verifying these identities.



 
Work with the right 
side.  Substitute

for  and
substitute 
for 
 
                      = 
Distribute out the
numerator:
                      = 
 
Put a 1 under the 
 so everything
will be a fraction 
                      = 


Invert the fraction
in the denominator 
and multiply:
 
                      = 
 
Swap the fraction factors:

                      =                    
 
 
Distribute:

                      =  

                      = 

                      = 

AND 


Work with the left side. 
Square out the two 
binomials:

 =




 


Use the identity  and
replace  by 



Distribute:



Combine like terms:



Edwin

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