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Question

If 2 cos x +sin x =1 then 7 cos x + 6 sin x=___


A

6

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B

2

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C

1

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D

3

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Solution

The correct options are
A

6


B

2


I = 7 cos x +6 sin x
= 6 (2 cos x + sin x)-5 cos x.
= 6-5 cos x.
Now, 2 cos x +sin x =1
sin x=12 cos xsin2x=1+4 cos2x4 cos x.1sin2x+4 cos2x4 cos x=05cos2x4cosx=0
cos x=0 or 45
I=6 or 2


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