Maths-
General
Easy

Question

# Statement-I : If sin x + cos x =  then Statement-II : AM ≥ GM

Hint:

## The correct answer is: Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I.

### Here, we have to find the which statement is correct and if its correct explanation or not.Firstly, Statement-I: If sinx + cosx = , x ∈ [ 0, π ] then x = , y = 1Here, we have,sinx + cosx = we know cosx + sinx ≤ 2 and , assuming y>0and in x∈[0,π] equality only exit if x= and y=1 as sin  +cos  = and =2 … (1)when substituted in given equation sinx + cosx = ⇒ √2 = √2 for these values it satisfies the equation thus, solution is, x=, y=1Therefore, statement-I is correct.Now,Statement-II: AM ≥ GMFor all,We know that the inequality relation between AM and GM isLet a1, a2…, can be n positive real numbers. The Arithmetic Mean and Geometric Mean defined as:AM =(a1+a2+⋯+an)/nGM =The AM–GM inequality states thatAM ≥ GMTherefore, Statement-II is correct, but it is not explanation of statement-I.The correct answer is, Statement-I is true, Statement-II is true; Statement-II is NOT a 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, Start solving first Statement and try to prove it. Then solve the Statement-II. Always, the AM–GM inequality states that AM ≥ GM.