Sin theta+2cos theta=1 prove that 2sin …
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Posted by Siddhant Shukla 5 years, 11 months ago
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Sia ? 5 years, 11 months ago
Given, sin θ + 2 cos θ = 1
On squaring both sides, we get
(sinθ+2cosθ)2=1
⇒sin2θ+4cos2θ+4sinθcosθ=1
⇒ 1 – cos2 θ + 4 (1 – sin2 θ) + 4 sin θ cos θ = 1 [∵sin2θ+cos2θ=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
⇒−(cos2θ+4sin2θ−4sinθcosθ)=−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
⇒2 sin θ – cos θ = 2
Hence proved.
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