Question

# Let be such that and Then cannot satisfy

Hint:

### In this question, we have to find the which region ϕ cannot satisfy. Now firstly, solve the given equation and find the value θ and ϕ and find the range of ϕ . If the given option is cannot match with the range then it will be our answer.

## The correct answer is:

### Here we have to find the which region ϕ cannot satisfy.

Now we have,

Given equation

⇒2cosθ (1−sin ϕ) =sin^{2}θ(x cos ϕ)−1 [since, tan x + cot y = 2/sin2x]

⇒2cosθ−2cossin ϕ =2sinθcos ϕ −1

⇒2cosθ+1=2sin(θ+ ϕ) .....(i)

Also given that tan(2π−θ)>0

⇒tanθ<0.....(1)

−1<sinθ<− √3/2

⇒θ ϵ (3Π/2, 5Π/3) .....(2)

So, ′θ′ is in 4th quadrant ⇒ L.H.S. of equation (i) will be positive.

1<2cosθ+1<2

⇒1<2sin(θ+ ϕ)<2

⇒21<sin(θ ϕ)<1

⇒2π+π/6 < θ + ϕ < 5π/6 +2π

⇒ 2π +π/6 − θmax < ϕ <2π+ 5π/6 −θmin

⇒ π/2 < ϕ < 4π/3

Therefore, ϕ satisfy itself from π/2 to 4π/3 .

The correct answer is 0 < ϕ < 4π/3 , 3π/2 < ϕ < 2π and 4π/3 < ϕ < 3π/2.

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 = .

### Related Questions to study

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

The number of solutions of the pair of equations in the interval [0, 2] is

The number of solutions of the pair of equations in the interval [0, 2] is

### Quantitative estimation of can be made by in acidified medium. In which medium it can be estimated by ?

### Quantitative estimation of can be made by in acidified medium. In which medium it can be estimated by ?

### If then the value of is equal to

### If then the value of is equal to

### If , then the intervals of values of for which , is

### If , then the intervals of values of for which , is

### . X is an unsaturated gaseous hydrocarbon. Find X?

### . X is an unsaturated gaseous hydrocarbon. Find X?

### The eq. wt. of in the reaction, is/are:

### The eq. wt. of in the reaction, is/are:

Which statement(s) is/are wrong?

Which statement(s) is/are wrong?

To solve a trigonometric inequation of the type sin x ≥ a where |a| ≤ 1, we take a hill of length 2 in the sine curve and write the solution within that hill. For the general solution, we add 2n. For instance, to solve , we take the hill over which solution is The general solution is , n is any integer. Again to solve an inequation of the type sin x ≤ a, where |a| ≤ 1, we take a hollow of length 2 in the sine curve. (since on a hill, sinx ≤ a is satisfied over two intervals). Similarly cos x ≥ a or cosx ≤a, |a| ≤ 1 are solved.

Solution to the inequation must be

To solve a trigonometric inequation of the type sin x ≥ a where |a| ≤ 1, we take a hill of length 2 in the sine curve and write the solution within that hill. For the general solution, we add 2n. For instance, to solve , we take the hill over which solution is The general solution is , n is any integer. Again to solve an inequation of the type sin x ≤ a, where |a| ≤ 1, we take a hollow of length 2 in the sine curve. (since on a hill, sinx ≤ a is satisfied over two intervals). Similarly cos x ≥ a or cosx ≤a, |a| ≤ 1 are solved.

Solution to the inequation must be

Which of the following compounds does not give halo form reaction?

Which of the following compounds does not give halo form reaction?