Question

Statement-I : In (0, ), the number of solutions of the equation is two

Statement-II : is not defined at

- Statement-I is True, Statement-II is True; Statement-II is a 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 statements. 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-I: In (0, π ) , the number of solutions of the equation tanθ + tan2θ +tan 3θ = tanθ tan2θ tan3θ is two

tanθ + tan 2θ + tan 3θ = tanθ tan2θ tan3θ

⇒tanθ + tan2θ = −tan3θ(1−tanθ+tan2θ)

⇒ (1−tanθtan2θ)/(tanθ+tan2θ)) = −tan3θ

⇒ tan3θ=tan(−3θ)

⇒ 3θ=nπ−3θ

⇒ 6θ=nπ ∀ n ∈ I or n=1,2,3,4,5

⇒ θ=6nπ

As 0<θ<π

∴θ=,,,,

However, tanθ &tan3θ are not defined at , , respectively

explanation of Statement-I & , are the only two solutions of equations.

Statement-II: tan 6 θ is not defined at θ = (2n + 1) , n ∈ I

Here statement- II is correct θ is not defined at θ = (2n + 1)

But it not the explanation of the Statement-I.

Therefore, 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, it has 5 solutions, but tanθ &tan3θ are not defined at , , . respectively so it remains only 2.

### Related Questions to study

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Statement-II : AM ≥ GM

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.

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### if

### if

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### if

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### if

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### if

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