Question

If sin + 2 cos = 1, then prove that 2 sine - cos = 2.​

Answer 1

Answer:

sin + 2 cos = 1

sin + cos = 1 - cos

squaring both side

sin^2 + cos^2 + 2 sin cos = 1 + cos^2 - 2 cos

1 + 2 sin cos = 1 + cos^2 - 2 cos

2 sin cos + 2 cos = cos^2

cos ( 2sin + 2) = cos ^2

2 sin + 2 = cos

2 sin - cos = 2

proved