SOlve the given equations squareroot 2 cos theta 1 0 ratio

SOlve the given equations.

squareroot 2 cos theta + 1 = 0 (rationalize to get a value we know) sin^2 x - sin x - 2 = 0

Solution

1. sqrt2 cos theta +1=0

      sqrt2 cos theta=-1

cos theta=-sqrt2/2

theta=cos^-1(-sqrt2/2)

theta= 3pi/4, 5pi/4

2. sin²x - sinx -2=0

    sin²x -2sinx + sinx -2=0

   sinx(sin x-2 )+1(sinx-2)=0

(sinx-2)(sinx +1)=0

sinx=2   or sinx=-1

sin x=-1

x=sin^-1-1

x= 3pi/2