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Question

The minimum and maximum values of sin(x+π4)sin(xπ4) are

A
1,1
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B
12,12
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C
32,32
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D
14,14
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Solution

The correct option is B 12,12
Given

sin(x+π4)sin(xπ4)

we know that

sin(A+B)sin(AB)=sin2Asin2B

sin(x+π4)sin(xπ4)=sin2xsin2π4

=sin2x(12)2

=sin2x12

But

sinx lies in [1,1]

1sinx+1


So,
0sin2x1

012sin2x12112

12sin2x1212

The function sin(x+π4)sin(xπ4) has the
minimum values: 12

maximum values: 12

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