Question

Could someone please explain the answer to this question to me?

Answer 1

`+-sqrt10/4`

Explanation:

`"using the "color(blue)"half angle formula for cos"`

`•color(white)(x)cos(theta/2)=+-sqrt((1+costheta)/2)`

`costheta=1/sectheta=1/4`

`0<= theta<=2pirArr0<=theta/2<=pi`

`cos((theta)/2)=+-sqrt((1+1/4)/2)`

`color(white)(xxxxxx)=+-sqrt(5/8)`

`color(white)(xxxxxx)=+-sqrt5/(2sqrt2)xxsqrt2/sqrt2=+-sqrt10/4`