SOLUTION: esatblish each idenntity cot theta - tan theta over cot theta + tan theta = cos 2theta

Question 703820: esatblish each idenntity

cot theta - tan theta over cot theta + tan theta = cos 2theta
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
cot theta - tan theta over cot theta + tan theta = cos 2theta
use x for theta
(cotx-tanx)/(cotx+tanx)=cos2x
start with left side:
(cotx-tanx)/(cotx+tanx)
=[(cosx/sinx)-(sinx/cosx)]/[(cosx/sinx)+(sinx/cosx)]
=[(cos^2x-sin^2x)/(sinxcosx)]/[(cos^2x+sin^2x)/(sinxcosx)]
sinxcosx cancels out, (cos^2x+sin^2x)=1
=(cos^2x-sin^2x)
=cos2x
verified: left side=right side
RELATED QUESTIONS
csc^2theta-cot^2theta/cot(theta)=tan(theta) (answered by lwsshak3)

cos^2theta sectheta= A. tan theta B. cot theta C. sin theta D. cos theta E. csc theta... (answered by texttutoring)

establish each identity A) sec^4 theta - sec^2 theta = tan^4 theta + tan^2 theta (answered by solver91311)

Verify the identity. Justify each step. tan theta + cot theta = 1/sin theta cos... (answered by KMST)

establish each identity A) 1 + tan theta over 1 - tan theta = cot theta + 1... (answered by lwsshak3)

tan(48)=cot(theta) (answered by jim_thompson5910)

Tan theta times csc^2 theta - tan theta = cot theta (answered by MathLover1)

Tan theta + cot theta=tan theta csc^2... (answered by Boreal)

PROVE TRIGONOMETRY IDENTITIES Sin(theta) + tan(theta) -----------------------... (answered by josgarithmetic)