Question

if sina + 2cosa = 1
then prove
LHS 2SINA-COSA = RHS 2

Answer 1

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.