Question

Sin A + 2 cos A = 1 then prove that 2 sin A minus cos A = 2

Answer 1

As sin + 2cos = 1
By squaring
sin² + 4cos² + 4 *sin * cos =1
(1-cos²) + 4* (1- sin²) + 4* sin * cos = 1
1 - cos² + 4 - 4* sin² + 4* sin * cos = 1
By multiplying both sides by -1, we get
cos² - 4 + 4* sin² - 4 * sin * cos = 0
cos² + 4* sin² - 4* sin * cos = 4
(2 * sin - cos )² = (2)²
Square root both the side
Therefore 2sin - cos = 2
(proved)
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Answer 2

Answer:

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Step-by-step explanation:

Hey I'm attaching two ways might they help.

First step is bit easier.

Second step is longer and bit confusing.