Question

Question #c7c6a

Answer 1

`theta=pi/2+2pik`

Explanation:

`costheta/(sinthetacostheta)=1`

`costheta=sinthetacostheta`

`1=sintheta`

To solve for `theta`, we need to find where on the unit circle that the height is `1`, which is at:

![https://www.desmos.com/calculator]()

`(0,1)` is at the rotation `pi/2` (or `90^@`), so that is the solution. Since the answer is the same after any full rotation, we add `2pik` (`k` is any integer) to represent all the possible solutions even after adding or subtracting any full rotation. The final answer is:

`theta=pi/2+2pik`

Answer 2

See the answer below...

Explanation:

`costheta/(sinthetacostheta)=1`

`=>costheta=sintheta cos theta`

`=>costheta-sintheta cos theta=0`

`=>costheta(1-sintheta)=0`

• Either,
  `costheta=0=cos(pi/2)color(red)(=>)color(red)(ul(bar(|color(green)(theta=2npi+-(pi/2))|`

• Or,
  `(1-sintheta)=0color(red)(=>)sintheta=1=sin(pi/2)color(red)(=>)color(red)(ul(bar(|color(green)(theta=((4n+1)pi)/2)|)))" ""always "(n in I)`

Hope it helps...
Thank you...