If f(x)= ∣∣
∣∣13cosx1sinx13cosx1sinx1∣∣
∣∣, then which of the following is/are correct ?
A
f(x) has maximum value 12
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B
f(x) has maximum value 10
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C
f (x) has maximum value −10
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D
f (x) has minimum value 0
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Solution
The correct options are B f(x) has maximum value 10 D f (x) has minimum value 0 f(x)=8cos2x−3sin2x+1 This can be written as f(x)=4cos2x−3sin2x+5 Differentiating with respect to x and simplifying gives us. tan2x=−34 hence the sets of values will be sin2x=35, cos2x=−45 or sin2x=−35, cos2x=45 Therefore after substituting, we get the minimum and maximum values as 0 and 10 respectively.