Verify the identity using one side

Calculus
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cotx = (1 + cos2x)/(sin2x)

Mar 20th, 2015

Note that, by the double-angle formulas for sine and cosine: 
i) cos(2x) = 2cos^2(x) - 1 
ii) sin(2x) = 2sin(x)cos(x). 

So, we have: 
RHS = [1 + cos(2x)]/sin(2x) 
= [1 + 2cos^2(x) - 1]/[2sin(x)cos(x)], from the above identities 
= 2cos^2(x)/[2sin(x)cos(x)] 
= cos(x)/sin(x), by canceling 2cos(x) 
= cot(x) 
= RHS. 

Mar 20th, 2015

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