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Question

The equation 4sin(x+π3)cos(xπ6)=a2+3sin2xcos2x has a solution if the value of a is

A
2
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B
0
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C
2
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D
a[2,2]
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Solution

The correct options are
A 2
B 0
C a[2,2]
D 2
Given equation 4sin(x+π3)cos(xπ6)=a2+3sin2xcos2x
4[sinxcosπ3+cosxsinπ3]×[cosxcosπ6+sinxsinπ6]=a2+3sin2xcos2x
4[12sinx+32cosx][32cosx+12sinx]=a2+3sin2xcos2x
3sin2x+3cos2x+sin2x=a2+3sin2xcos2x
cos2x+2=a2cos2x
cos2x=a222
1a2221
0a24
2a2.
all values of a given in (a), (b), (c), (d) satisfy this relation.

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