Question

6. If sin 0 + 2 cos 0 = 1 prove that 2 sin 0 - cos 0 = 2.​

Answer 1

Answer:

sin o=2

cos o=0

tan o=2/0

now,tan=p/b=2/0

p=2 and b=0

please mark as brainlist

Answer 2

Given, sin θ + 2cos θ = 1

Squaring on both sides, we get

Now, (sin θ + 2cos θ)2 = 12

=> sin2 θ + 4cos2 θ + 4*sin θ * cos θ = 1

=> 1 - cos2 θ + 4(1 - sin2 θ) + 4 * sin θ * cos θ = 1 [Since sin2 θ + cos2 θ = 1]

=> 1 - cos2 θ + 4 - 4 * sin2 θ + 4 * sin θ * cos θ = 1

=> 5 - cos2 θ - 4 * sin2 θ + 4 * sin θ * cos θ = 1

=> 5 - 1 = cos2 θ + 4 * sin2 θ - 4 * sin θ * cos θ

=> cos2 θ + 4 * sin2 θ - 4 * sin θ * cos θ = 4

=> 4 * sin2 θ + cos2 θ - 4 * sin θ * cos θ = 22

=> (2sin θ - cos θ)2 = 22

=> 2sin θ - cos θ = ±2

Hence proved.