Question

Find the sum of the three smallest positive values of theta such that 4(cos^2)(2theta-pi) =3. (Give your answer in radians.)
LaTEX: Find the sum of the three smallest positive values of $\theta$ such that $4\cos^2(2\theta-\pi) =3$. (Give your answer in radians.)

Answer 1

4cos^2(2θ-π) = 3
cos^2(2θ-π) = 3/4
since cos(a-b) = cosa cosb + sina sinb, cos(2θ-π) = -cos(2θ)
cos^2(2θ) = 3/4
cos(2θ) = ±√3/2
now cos π/6 = √3/2
so, 2θ = π/6, 5π/6, 7π/6, 11π/6
θ = π/12, 5π/12, 7π/12, ...
their sum is 13π/12