SOLUTION: Verify that each equation is an identity
(2cos^2 (X/2)) (tan X) = tan X + sin X
1-tan^2 (t/2) = ((2cos t)/(1+cos t))
Algebra ->
Trigonometry-basics
-> SOLUTION: Verify that each equation is an identity
(2cos^2 (X/2)) (tan X) = tan X + sin X
1-tan^2 (t/2) = ((2cos t)/(1+cos t))
Log On
Question 799820: Verify that each equation is an identity
(2cos^2 (X/2)) (tan X) = tan X + sin X
1-tan^2 (t/2) = ((2cos t)/(1+cos t)) Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Verify that each equation is an identity
..
(2cos^2 (X/2)) (tan X) = tan X + sin X
Identity:cos(x/2)=√((1+cosx)/2)
start with left side:
2((1+cosx)/2)(tanx)=tanx+tanxcosx=tanx+(sinx/cosx)*cosx=tanx+sinx
verified:left side=right side
..
1-tan^2 (t/2) = ((2cos t)/(1+cos t))
Identity: tan(t/2)=sint/(1+cost)
start with left side:
1-(sint/(1+cost))^2=1-(sin^2t)/(1+cost)^2
=((1+cos^t)^2-sin^2t)/(1+cost)^2
=(1+2cost+cos^2t-1+cos^2t)/(1+cost)^2
=(2cost+2cos^2t)/(1+cost)^2
=2cost(1+cost)/(1+cost)^2=2cost/(1+cost)
verified: left side=right side
(