cos-3-2sin-2-3-0-2pi-what-is-

Question Number 80739 by jagoll last updated on 05/Feb/20

\cos^{3} θ + 2 \sin^{2} θ = 3 \bar{} θ \in (0, 2 π)

w h a t i s θ ?

Commented by mr W last updated on 06/Feb/20

n o s o l u t i o n! b e c a u s e L H S m a x = 2 < R J S!

Commented by hknkrc46 last updated on 06/Feb/20

{s i n}^{2} θ = 1 - {c o s}^{2} θ

{c o s}^{3} θ + 2 (1 - {c o s}^{2} θ) = 3

{c o s}^{3} θ + 2 - 2 {c o s}^{2} θ = 3

{c o s}^{3} θ - 2 {c o s}^{2} θ = 1

{c o s}^{2} θ (c o s θ - 2) = 1

- 1 ⩽ c o s θ ⩽ 1 \Rightarrow - 3 ⩽ c o s θ - 2 ⩽ - 1

\Rightarrow {c o s}^{2} θ < 0 \Rightarrow θ \notin (0, 2 π)