Find the solution of the equation that are in the internal 0

Find the solution of the equation that are in the internal [0, 2pi). 2 cos^2 theta + cos theta = 0 If sin alpha = -4/5 and sec beta = 5/3 for a third-quadrant and alpha and first-quadrant angle beta, find sin(alpha + beta) tan(alpha + beta) the quadrant containing the angle alpha + beta

Solution

2cos²theta + cos theta=0

cos theta(2cos theta + 1)=0

cos theta=0 and 2cos theta+1=0

taking cos^-1 on both sides

theta = cos^-10    and theta= cos^-1(-1/2)

theta= pi/2,3pi/2 and theta= 2pi/3, 4pi/3

theta=pi/2, 2pi/3,4pi/3,3pi/2