Question

Question #7ec3c

Answer 1

`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))`

Answer 2

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...