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Question

If 2 cos x + sin x = 1, then value of 7 cos x + 6 sin x can be
  1. 2
  2. 6
  3. 3
  4. 1


Solution

The correct options are
A 2
B 6
If 2 cos x + sin x = 1, then value ………
2 cos x = 1 – sin x
On squaring 4cos2x=12sinx+sin2x
5sin2x2sinx3=0sinx=1,35
When sin x = 1,  then cos x = 0 and so 7 cos x + 6 sin x = 6
When sin x=35, then cos x=45
cos x + 6 sin x = 2
Hence 7 cos x + 6 sin x = 6 or 2

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