Trigenometry question?

Question

y= 2cos^2t+cost-1 
Algebraically find all the zeros in the equation over the domain of all reals. 
Express your answer in term of pi.

Answer 1

The trigonometric equation is y = 2cos² t + cos t - 1.

Let, 2cos² t + cos t - 1 = 0

By factor by grouping.

2cos² t + 2cos t - cos t - 1 = 0

2cos t(cos t + 1) - 1(cos t + 1) = 0

Factor : (cos t + 1)(2cos t - 1) = 0

Apply zero product property.

cos t + 1 = 0 and 2cos t - 1 = 0

cos t = - 1 and cos t = 1/2

t = cos^-1 (- 1) and t = cos^-1 (1/2)

t = cos^-1 (cos (±π)) and t = cos^-1 (cos (±π/3))

t = ±π and t = ±π/3.

The solutions of the equation are t = 2nπ ± π and t = 2nπ ± π/3, where n is an integer.