Maths-
General
Easy

Question

# Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zeroStatement-II : Since |sin x| ≤ 1

Hint:

## 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 = 2x + 2-x is zero.2x + 2-xsinx = 2x + 2-xLHS:We know that, for all value , -1 ≤ sinx ≤ 1 So value of sinx is between 1 to -1.RHS :2x + 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 zeroNow, 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 | ≤ 1Hence, | sinx | ≤ 1Therefore, 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.