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Find number of solutions of equation s...

Find number of solutions of equation
`sin^(2) theta- 4/(sin^(3) theta-1)=1- 4/(sin^(3) theta-1), theta in [0, 6pi]`.

Text Solution

Verified by Experts

The correct Answer is:
Three solutions
We have
`sin^(2) theta- 4/(sin^(3) theta-1)=1- 4/(sin^(3) theta-1)`, where `sin theta ne 1`
`:. sin^(2) theta=1, sin theta ne 1`
`:. sin theta=-1`
Thus, there are three values of `theta` one each in intervals `[0, 2pi], [2pi, 4pi]` and `[4pi, 6pi]`
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