Maths-
General
Easy

Question

# Statement-I : In (0, ), the number of solutions of the equation  is twoStatement-II :  is not defined at

Hint:

## 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=6nπAs 0<θ<π∴θ=,,,,However, tanθ &tan3θ are not defined at , ,  respectivelyexplanation 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.