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
Statement-I : If sin x + cos x = 
then 
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.
Statement-I : If sin x + cos x = then
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.
Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zero
Statement-II : Since |sin x| ≤ 1
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, -1 ≤ sinx ≤ 1 for all value, remember that.
Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zero
Statement-II : Since |sin x| ≤ 1
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, -1 ≤ sinx ≤ 1 for all value, remember that.
if
if
if
if
if
if
if
if
if
In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.
if
In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.
Number of ordered pairs (a, x) satisfying the equation 
is
Number of ordered pairs (a, x) satisfying the equation is
The general solution of the equation, 
is :
The general solution of the equation, is :
The noble gas used in atomic reactor ,is
The noble gas used in atomic reactor ,is
Which compound does not give 
on heating?
Which compound does not give on heating?
In the interval 
the equation 
has
In this question, we have to find type of solution, here, we know if 
then we can take antilog, b = ca, and cos2 θ = 1 – 2 sin2 θ . Remember these terms and find the solution easily.
In the interval the equation has
In this question, we have to find type of solution, here, we know if then we can take antilog, b = ca, and cos2 θ = 1 – 2 sin2 θ . Remember these terms and find the solution easily.
If 
,then
In this question, we have to find the where is θ lies. Here, always true for sinx ≥ 0 otherwise it is true for x=0,,
,2π and since we also need x≠, for tanx and x≠0,2π for cotx all the solutions.
If ,then
In this question, we have to find the where is θ lies. Here, always true for sinx ≥ 0 otherwise it is true for x=0,,,2π and since we also need x≠, for tanx and x≠0,2π for cotx all the solutions.
Number of solutions of the equation 
in the interval [0, 2] is :
Number of solutions of the equation in the interval [0, 2] is :
If 
,then
In this question, we have given equation, where we have to find where the θ belongs. For all value of sin θ cos θ = 
so θ always lies between ( 0 , ) .
If ,then
In this question, we have given equation, where we have to find where the θ belongs. For all value of sin θ cos θ = so θ always lies between ( 0 , ) .
