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 =

Statement-I is true, Statement-II is true ; Statement-II is 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

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

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

Hint:

### Here two statements are given. 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 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, sin^{2}x + cos^{2}x = 1 and sin^{2}x = 2sinx.cosx]

= [ a^{2} + b^{2} + 2ab = (a+b)^{2}]

Now , at x = , we have,

=

=

=

=

=

= 2

Therefore, = 2 is True.

Now for statement 2 – The maximum value of sinx + cosx occur when x = ,

Let y = sinx + cosx

= cosx – sinx

= 0

cosx = sinx ,

tanx = 1 = tan

we know, x = n π +

in 0 ≤ x ≤

x =

= -sinx – cosx < 0

therefore, 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.

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