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Cool goIITian

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cos²A-6sinAcosA+3sin²A+2

= cos²A+sin²A-3.2sinAcosA+2+2sin²A

=1-3sin2A+2sin²A+2

=3-3sin2A+2(1-cos²A)

=3-3sin2A+2-2cos²A

=5-3sin2A-2cos²A+1-1

=4-3sin2A-(2cos²A-1)

=4-3sin2A-cos2A

=-3sin2A-cos2A+4

minimum or maximum value of asinx+bcosx+c =c+_

a²+b²

manimum and maximum of -3sin2A-cos2A+4 = 4+_

(-3)²+(-1)²

=4+_

hence minimum value of given expression is 4-

maximum value of given expression is 4+

10 (check the max value also)

Hence problem is completed

Bye........................................

Note:- +_ shows plus or minus

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