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How many solutions will 2sinx(3cosx−1)=0

How many solutions will 2sinx(3cosx−1)=0

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Answer #1

If there are no restrictions for x, there are infinite number of solutions to the given equation. If we need to find number of solutions inside a particular limit, there will be a definite number for the solution.

To get the solution clear, Consider the LHS of the given equation:

The above will be zero in either of the following conditions:

1.

2. or

Sine function is zero for an infinite number of x, Also cosine function is 1/3 for infinite number of x too. So we can conclude that number of solutions to the given equation is infinity.

(But remember that if there were any limits given for x, then the answer would be a finite number)

Concluding, as there are no limits for x, the number of solutions is infinity.

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