Question
Wed August 22, 2012 By: Akriti

If SinA + 2CosA = 1 then prove that 2SinA-CosA = 2

Expert Reply
Wed August 22, 2012
Given, sin A + 2 cos A = 1
Squaring both sides, we get,
sin2A + 4 cos2A + 4sinA cosA = 1
4 cos2A + 4sinA cosA = 1 - sin2A = cos2A
3 cos2A + 4sinA cosA = 0                ... (i)
 
Now, (2sinA - cosA)2 = 4sin2A + cos2A - 4sinA cosA
                             = 4sin2A + cos2A + 3cos2A          [Using (i)]
                             = 4 (sin2A + cos2A) = 4
Thus, 2sinA - cosA = 2
Hence, proved.
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