Question

Given that sin theta + 2 cos theta = 1 , then prove that 2 sin theta -cos theta = 2

Answer 1

Sol. sin θ + 2 cos θ = 1 [Given]
On squaring both sides, we get
(sin θ)2
+ (2 cos θ)2
+ 2(sin θ) (2 cos θ) = 1
⇒ sin2
θ + 4 cos2
θ + 4 sin θ cos θ = 1
⇒ 1 – cos2
θ + 4 (1 – sin2
θ) + 4 sin θ cos θ = 1
⇒ 1 – cos2
θ + 4 – 4 sin2
θ + 4 sin θ cos θ = 1
⇒ –cos2
θ – 4 sin2
θ + 4 sin θ cos θ = –4
⇒ cos2
θ + 4 sin2
θ – 4 sin θ cos θ = 4
⇒ (cos θ)2
+ (2 sin θ)2
– 2(cos θ) (2 sin θ) = 4
⇒ (2 sin θ – cos θ)2
= 22
Taking square root both sides, we have
2 sin θ – cos θ = 2
Hence, proved.
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Answer 2

Answer:

Step-by-step explanation:

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