Maths-
General
Easy

Question

# Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is  only.Statement - II The maximum value of sin x + cos x occurs when x =

Hint:

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

### Here we have to find the which statement is correct and if its correct explanation or not.Firstly, statement 1: The value of x for which = 2, when 0 ≤ x ≤, is only.So, we have,  = [ since, sin2x + cos2x = 1 and sin2x = 2sinx.cosx]= [ a2 + b2 + 2ab = (a+b)2]Now , at x = , we have,=== = = = 2Therefore, = 2 is True.Now for statement 2 – The maximum value of sinx + cosx occur when x = ,Let y = sinx + cosx = cosx – sinx = 0cosx = sinx ,tanx = 1 = tan we know, x = n π + in 0 ≤ x ≤ x = = -sinx – cosx < 0therefore, sinx + cosx is maximum at π/4. And statement 2 is correct explanation because √2 is maximum value in π/4. And it is the only case which satisfies the statement 1 at π/4.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.