Question

if sin+2cos=1 THEN PROVE THAT 2sin-cos=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)

Answer 2

this is the required answer