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Question

Let f(x)=(sin1x)2(cos1x)2. If range of f equals [aπ24,bπ24] where a,bZ, then the value of ba is

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Solution

Given,
f(x)=(sin1x)2(cos1x)2=(sin1x+cos1x)(sin1xcos1x)=π2(sin1x(π2sin1x))f(x)=π2(2sin1xπ2), x[1,1]
As f is increasing function,
so, fmax=f(1)=π2(2(π2)π2)=π24
and fmin=f(1)=π2(2(π2)π2)=3π24
Hence, range of f is[3π24,π24]
a=3 and b=1
ba=1(3)=4

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