Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
i got it-
(sinθ + 2cosθ)2 = 12
(sinθ + 2cosθ)2 + (2sinθ – cosθ)2 = 1 + (2sinθ – cosθ)2
5sin2θ + 5cos2θ = 1 + (2sinθ – cosθ)2
5 - 1 = (2sinθ – cosθ)2
root4 = 2sinθ – cosθ
or, 2sinθ – cosθ = 2.