Maths-

General

Easy

Question

Statement - I For any real value of or the value of the expression 0 or y≥2 (either less than or equal to zero or greater than or equal to two)

Statement - II for all real values of .

- 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

Hint:

### In this question, given two statement. 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-1: For any real value θ ≠ (2n + 1) π or (2n + 1) , nϵ I, the value of expression

y =( cos^2 θ -1)/ ( cos^2 θ + cos θ) is y ≤ 0 or y ≥ 2 ( either less than or equal to zero or greater than to two.

We have,

Or

As the range of secx is ≤−1 and ≥1

Or

1−y<−1 and 1−y>1

Or

y>2 and y<0.

So statement I is False,

Statement-II – secθ∈(−∞,−1]∪[1,∞) for all real values of θ.

So we know that for all , range of sec x ≤−1 and ≥1,

So secθ∈(−∞,−1]∪[1,∞) for all real values of θ.

Therefore, statement-II is correct.

The correct answer is Statement – I is false, Statement – II is true.

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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