Solve one equation below by showing all steps Support your a

Solve one equation below by showing all steps. Support your answer by stating the property, formula, or the theorem used. 4 cos^2 theta + 4 cos theta = 1 3 cot^2 theta - 3 cot theta - 1 = 0 2 cos^2 theta + 2 cos theta + 1 = 0 2 sin theta = 1 - 2 cos theta

Solution

36.

4cos²+4cos=1

let cos=x => cos²=x²

4x²+4x=1

=>x²+x=1_/4

=>x²+x+(1_/4)=(1_/4)+(1_/4)

=>(x+(1_/2))²=(1_/2)

=>(x+(1_/2))=(-2_/2),(x+(1_/2))=(2_/2)

=>x=((-1-2)_/2),x=((-1+2)_/2)

=>cos=((-1-2)_/2),cos=((-1+2)_/2)

=> =2n -cos^-1((-1-2)_/2), =2n +cos^-1((-1-2)_/2), =2n -cos^-1((-1+2)_/2), =2n +cos^-1((-1+2)_/2) ,where n is an integer