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.

### Related Questions to study

### If ,then

In this question, we have to find the where is θ lies. Here, always true for sinx ≥ 0 otherwise it is true for x=0,,,2π and since we also need x≠, for tanx and x≠0,2π for cotx all the solutions.

### If ,then

In this question, we have to find the where is θ lies. Here, always true for sinx ≥ 0 otherwise it is true for x=0,,,2π and since we also need x≠, for tanx and x≠0,2π for cotx all the solutions.

Number of solutions of the equation in the interval [0, 2] is :

Number of solutions of the equation in the interval [0, 2] is :

### If ,then

In this question, we have given equation, where we have to find where the θ belongs. For all value of sin θ cos θ = so θ always lies between ( 0 , ) .

### If ,then

In this question, we have given equation, where we have to find where the θ belongs. For all value of sin θ cos θ = so θ always lies between ( 0 , ) .

### If

### If

The most general solution of the equations is

The most general solution of the equations is

The general solution of the equation, is

The general solution of the equation, is

The most general solution of cot = and cosec = – 2 is :

In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.

The most general solution of cot = and cosec = – 2 is :

In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.

### Let S = The sun of all distinct solution of the equation

### Let S = The sun of all distinct solution of the equation

### A wave motion has the function The graph in figure shows how the displacement at a fixed point varies with time Which one of the labelled points shows a displacement equal to that at the position at time

### A wave motion has the function The graph in figure shows how the displacement at a fixed point varies with time Which one of the labelled points shows a displacement equal to that at the position at time

### For , the equation has

### For , the equation has

### Which of the following pairs of compounds are functional isomers?

### Which of the following pairs of compounds are functional isomers?

### Let be such that and Then cannot satisfy

In this question we have to find the the which region ϕ cannot satisfy. In this question more than one option is correct. Here firstly solve the given equation. Remember that, , tan x + cot x = .

### Let be such that and Then cannot satisfy

In this question we have to find the the which region ϕ cannot satisfy. In this question more than one option is correct. Here firstly solve the given equation. Remember that, , tan x + cot x = .

The number of all possible values of , where 0< < , which the system of equations has a solution with , is

The number of all possible values of , where 0< < , which the system of equations has a solution with , is

Roots of the equation are

Roots of the equation are