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Question

Assertion :The value of π/20sin6xdx=5π16 Reason: If n is even, then π/20sinnxdx equals n1nn3n2n5n4...12×π2

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 correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct.
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Solution

The correct option is D Assertion is incorrect but Reason is correct.
I=π20sin6(x).dx
=π02sin6(π2x).dx
=π20cos6(x).dx
Hence
2I=π20sin6(x)+cos6(x).dx
sin6(x)+cos6(x)=[(sin2(x)+cos2(x))(sin4(x)+cos4(x)sin2(x).cos2(x))]
=sin4(x)+cos4(x)sin2(x).cos2(x))
=(sin2(x)+cos2)22sin2x.cos2xsin2(x)cos2(x)
=13sin2x.cos2x
=13sin22(x)4
=13(1cos4x)8
=58+3cos4x8
Hence
2I=π2058+3cos4x8.dx
2I=5π16
I=5π32.
Hence Assertion is false.

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