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

Asked by Akriti | 22nd Aug, 2012, 05:30: PM

Expert Answer:

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.

Answered by  | 22nd Aug, 2012, 11:05: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.