For which value(s) of \(θ\) (where \(0^\circ ≤ θ ≤ 90^\circ\)) will \(2\sinθ\cosθ = \cosθ\) be true?

Q.For which value(s) of \(θ\) (where \(0^\circ ≤ θ ≤ 90^\circ\)) will \(2\sinθ\cosθ = \cosθ\) be true?

\(2\sinθ\cosθ = \cosθ\) i.e., \(2\sinθ\cosθ - \cosθ = 0\) i.e., \(\cosθ(2\sinθ - 1) = 0\) \(\therefore\) Either \(\cosθ = 0 = \cos90^\circ\) i.e., \(θ = 90^\circ\) Or, \(2\sinθ - 1 = 0\) i.e., \(2\sinθ = 1\) i.e., \(\sinθ = \cfrac{1}{2} = \sin30^\circ\) i.e., \(θ = 30^\circ\) \(\therefore\) The value of \(θ\) will be either \(30^\circ\) or \(90^\circ\).