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Question

If the product (sin1)(sin3)(sin5)(sin7).........(sin89)=12n, then find the value of n.

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Solution

sin1sin3sin5.........sin89=12n

sin1sin2sin3.....sin88sin89sin2sin4sin6.....sin88=12n

sin1sin89sin2sin88....sin44sin(46)sin45sin2sin4sin6.....sin88=12n

sin1sin(901)sin2sin(902).................sin44sin(9044)sin45sin2sin4sin6.........sin88=12n

sin1cos1sin2cos2.................sin44cos44sin45sin2sin4sin6.........sin88=12n ...........cosA=sin(90˚A)

sin2sin4...........sin88sin45244(sin2sin4...........sin88=12n ...............[sin2x=2sinxcosx]

12442=12n

n=4412=892

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