Question #7ec3c

2 Answers
Nghi N
Feb 13, 2018

#pi/3; (5pi)/3#

Explanation:

#2cos^2 (t/2) - 3cos t = 0#
Using identity #(1 + cos 2a = 2 cos^2 a)#, replace in the equation
#2cos^2 (t/2)# by #(1 + cos t)#.
We get:
1 + cos t - 3cos t = 0
#cos t = 1/2#
Trig Table and unit circle give 2 solutions:
#t = +- pi/3#, or
#t = pi/3#, and #t = (5pi)/3# (co-terminal to #(- pi/3))#

Sunayan S
Feb 13, 2018

Give a look here...

Reference proof:-

#costheta=cos^2(theta/2)-sin^2(theta/2)#
#=>costheta=cos^2(theta/2)-1+cos^2(theta/2)#
#=>costheta=2cos^2(theta/2)-1#

Explanation:

#2cos^2(theta/2)-3costheta=0#
#=>(costheta+1)-3costheta=0#
#=>2costheta=1#
#=>costheta=1/2#
#=>costheta=cos(pi/3)#
#=>theta=2npi+-(pi/3)" "[n in I]#

for#" "color(red)(n=0->theta=pi/3#
for#" "color(red)(n=1->theta=(5pi)/3#

Hope it helps...
Thnx...

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