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Question

If set of all values of x(π2,π2) satisfying |4sinx+2|<6 is (aπ24,bπ24), then the value of ab3=

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Solution

|4sinx+2|<6
6<4sin x+2<62(3+1)<4sin x<2(31)
(3+1)22<sinx<(31)22sin5π12<sinx<sinπ125π12<x<π12 for x(π2,π2)
Comparing with aπ24<x<bπ24, we get, a=10,b=2
ab3=1023=4

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