How do I solve this problem?
Prove the identity by changing the left side of the equation to show equivalency to the right side.
(1 + cos 2 theta) / (sin 2 theta) = cot theta

Question

How do I solve this problem?
Prove the identity by changing the left side of the equation to show equivalency to the right side. 
(1 + cos 2 theta) / (sin 2 theta)  = cot theta

imstuck · Answer

I think that's cos(2theta) [I'm going to call theta x cuz it's easier than theta].  So, I think that's (1+cos(2x))/sin(2x)=cot x.  I hope that is right cuz that's what I'm going off!  First of all, these are both double angle identities.  So we will change them to their simpler forms.$$\cos(2x)=2\cos ^{2}x-1$$and the double angle identity for sin(2x) is 2sinxcosx.  Now fill this into the equation using the substitutions:$$\frac{ 1+2\cos ^{2}x-1 }{ 2sinxcosx }$$The +1 and -1 in the numerator cancel each other out leaving you with $$\frac{ 2\cos ^{2}x }{ 2sinxcosx}$$The 2's cancel each other out, as does one of the cosx's, leaving us with $$\frac{ cosx }{ sinx }$$which is the same as cotangent x.

anonymous · Answer

Thank you so much! I've been having so much trouble with this problem, I was trying to use half angle identities instead of double.