SOLUTION: establish each identity cot(2 theta)= 1/2(cot theta

SOLUTION: establish each identity cot(2 theta)= 1/2(cot theta - tan theta)

Question 703821: establish each identity
cot(2 theta)= 1/2(cot theta - tan theta)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
establish each identity
cot(2 theta)= 1/2(cot theta - tan theta)
use x for theta
cot2x=1/2(cotx-tanx)
start with right side:
1/2(cotx-tanx)
=1/2[(cosx/sinx)-(sinx/cosx)]
=1/2[(cos^2x-sin^2x/sinxcosx)]
=(cos^2x-sin^2x)/2sinxcosx)
=cos2x/sin2x
=cot2x
verified: right side=left side
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