Question

If sin + 2 cos = 1 prove that 2 sin - cos = 2.

Answer 1

Answer:

solved

Step-by-step explanation:

If sin∝ + 2 cos∝ = 1 prove that 2 sin ∝- cos∝ = 2.

now

sin∝ + 2 cos∝ = 1

sin∝  = 1 - 2 cos∝

sin²∝ + cos²∝ = 1

( 1 - 2 cos∝ )² + cos²∝ = 1

5cos²∝ - 4cos∝ = 0

cos∝ = 0,0.8 ,  sin∝ = 1, 0.6

(cos∝ , sin∝) = ( 0,1) or  ( 0.8 , 0.6)

ist. case

2 sin ∝- cos∝ = 2 - 0 = 2 ,  correct

2nd case

2 sin ∝- cos∝ = 2*0.6 - 0.8 = 0.4 ≠ 2

only first case is o.k.