Question

Prove if
sinA + 2cosA = 1, then prove that
2sinA - cosA = 2

Answer 1

sin(A) = 1 - 2*cos(A) 

Squaring both sides: 

sin²(A) = 1 - 4*cos(A) + 4*cos²(A) 

1 - cos²(A) = 1- 4*cos(A) + 4*cos²(A) 

5*cos²(A) - 4*cos(A) = 0 

cos(A)*(5*cos(A) - 4) = 0 

cos(A) = 0 and cos(A) = 4/5 

When cos(A) = 0, sin(A) = 1 

2*sin(A) - cos(A) = 2(1) - 0 = 2