Question

# Assertion :Let f(x)=âˆ£âˆ£ âˆ£âˆ£0cosxâˆ’sinxsinx0cosxcosxsinx0âˆ£âˆ£ âˆ£âˆ£2If sin2x=1 then f(x)=2/3 Reason: f(x)=0 if sinx=cosx

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is incorrect but Reason is correct
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D
Assertion is correct but Reason is correct
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Solution

## The correct option is C Assertion is incorrect but Reason is correctMultiplication of two determinants leads usf(x)=∣∣ ∣∣1−yy−y1yyy1∣∣ ∣∣where y=sinxcosxUsing C1→C1−C2,C2→C2+C3 we getf(x)=(1+y)2∣∣ ∣∣10y−11y011∣∣ ∣∣=(1+y)2∣∣ ∣∣10y012y011∣∣ ∣∣(1+y)2(1−2y)when sin2x=1,y=1/2 and f(x)=0when sinx=cosx,1−2y=1−2sin2x=cos2x=0∴f(x)=0

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