If sinA + 2cosA = 1. Prove that 2sinA -cosA= 2.

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Solution

Given
sinA + 2cosA= 1

By squaring both sides,

sin²A + 4cos²A + 4sinA. cosA =1

(1-cos²A) + 4(1- sin²A) + 4. sinA. cosA = 1

1 - cos²A + 4 - 4 sin²A + 4. sinA. cosA = 1

By multiplying both sides by -1, we get

cos²A - 4 + 4 sin²A - 4.sinA. cosA = 0

cos²A + 4 sin²A - 4. sinA. cos A= 4

(2 sinA - cosA )² = (2)²

Square root both the side
Therefore

2sinA - cosA = 2

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