Question

Statement-I : The number of real solutions of the equation sin x = 2^{x} + 2^{–x} is zero

Statement-II : Since |sin x| ≤ 1

- Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I.
- Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I
- Statement-I is True, Statement-II is False
- Statement-I is False, Statement-II is True

Hint:

### In this question, given two statements. It is like assertion and reason. Statement1 is assertion and statement 2 is reason, Find the statement 1 is correct or not and the statement 2 correct or not if correct then is its correct explanation.

## The correct answer is: Statement-I is False, Statement-II is True

### Here , we have to find the which statement is correct and if its correct explanation or not.

Firstly ,

Statement-I : The number of real solutions of the equation sinx = 2^{x} + 2^{-x} is zero.

2^{x} + 2^{-xsinx} = 2^{x} + 2^{-x}

LHS:

We know that, for all value ,

-1 ≤ sinx ≤ 1

So value of sinx is between 1 to -1.

RHS :

2^{x} + 2^{-x} ,

The minimum value of this term is 2 if we put x = 0.

So here LHS ≠ RHS,

It has no solution,

So, Statement-I is True. Because its solution is zero

Now, we have

Statement-II: Since | sin | ≤ 1.

So, we know that for all value,

-1 ≤ sinx ≤ 1

So, value of sinx is between 1 to -1.

Now,

0 ≤ | sinx | ≤ 1

Hence, | sinx | ≤ 1

Therefore, Statement-II is also true, and it is correct explanation of Statement-I.

The correct answer is Statement-I is true, Statement-II is true; Statement-II is correct explanation for Statement-I.

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, -1 ≤ sinx ≤ 1 for all value, remember that.

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