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Question

If sin A + 2cos A = 1

Prove That 2sin A - cos A = 2

Please explain with full steps


Solution

Given, sinθ+2cosθ=1

On squaring both sides, we get;

(sinθ+2cosθ)2=1

sin2θ+4cos2θ+4sinθ.cosθ=1

(1cos2θ)+4(1sin2θ)+4sinθ.cosθ=1

[sin2θ+cos2θ=1]

cos2θ4sin2θ+4sinθ.cosθ=4

4sin2θ+cos2θ4sinθ.cosθ=4

(2sinθcosθ)2=4

[a2+b22ab=(ab)2]

2sinθcosθ=2
Here θ is used  instead of A

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