Question

In the interval the equation has

- no solution
- a unique solution
- two solutions
- infinitely many solutions

Hint:

### In this question, we have given that in the interval of . We have to find it which type of solution it has. We know that then we can take antilog, b = c^{a}. Using find the solution of equation.

## The correct answer is: a unique solution

### Here we have to find it which type of solution it has.

Firstly, we have given,

We know if then we can take antilog, b = c^{a}

So, we can write,

Cos^{2} θ = sin^{2} θ

1 – 2 sin^{2} θ = sin^{2} θ [ since, cos^{2} θ = 1 – 2 sin^{2} θ ]

3sin^{2} θ = 1

sin^{2} θ =

sin θ = ±

Base of log is never negative,

sin θ =

Therefore, it has only one solution, that means it has unique solution.

The correct answer is a unique solution.

In this question, we have to find type of solution, here, we know if then we can take antilog, b = c^{a}, and cos^{2} θ = 1 – 2 sin^{2} θ . Remember these terms and find the solution easily.

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