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Question

Number of solutions of the equation (2 cosec x1)13+(cosec x1)13=1 in (kπ,kπ) is 16, then the possible value of 'k' is

A
2
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B
4
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C
8
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D
16
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Solution

The correct option is D 16
Given that
(2 cosec x1)13+(cosec x1)13=1

Converting everything into sin x
(2sin x1)13+(1sin x1)13=1

Let sin x=s
(2s)13+(1s)13=s13....(i)

Cube both sides
32s +3(s(2s)(1s))13=s (...(i))
(s(2s)(1s))13=s1
s=1 (cube both the sides)
sin x=1

So, 1 solution in (π,π)

k solution in (kπ,kπ) k=16


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