Question
If 
,then
Hint:
In this question, we have given trigonometry function. Which is
and belongs to [ 0, 2 π]. We have to find where θ is belongs. Solve the function and find the answer.
The correct answer is:
Here , we have to find where θ lies in this equation.
Firstly, we have given
We know that,
= 1 + 2 sin θ cos θ
So, we can write, in eq (1)
sin θ cos θ - |sin θ| cos θ = 0
cos θ ( sin θ - | sin θ| ) = 0
hence, sin θ = | sin θ |
which is always true for sinx ≥ 0 otherwise it is true for x=0,
,
,2π
Therefore, since we also need x≠, for tanx and x≠0,2π for cotx all the solutions are given by x∈(0,π) with x≠
and x≠.
The correct answer is θ ϵ (0 ,π)- { ,}
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.
Related Questions to study
Number of solutions of the equation 
in the interval [0, 2
] is :
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If 
,then
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If ,then
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If 
If
The most general solution of the equations 
is
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is
The general solution of the equation, is
The most general solution of cot
=
and cosec = – 2 is :
In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.
The most general solution of cot = and cosec = – 2 is :
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Let S = 
The sun of all distinct solution of the equation 
Let S = The sun of all distinct solution of the equation
A wave motion has the function 
The graph in figure shows how the displacement 
at a fixed point varies with time 
Which one of the labelled points shows a displacement equal to that at the position 
at time 
A wave motion has the function The graph in figure shows how the displacement at a fixed point varies with time Which one of the labelled points shows a displacement equal to that at the position at time
For 
, the equation 
has
For , the equation has
Let 
be such that 
and 
Then 
cannot satisfy
In this question we have to find the the which region ϕ cannot satisfy. In this question more than one option is correct. Here firstly solve the given equation. Remember that, , tan x + cot x = 
.
Let be such that and Then cannot satisfy
In this question we have to find the the which region ϕ cannot satisfy. In this question more than one option is correct. Here firstly solve the given equation. Remember that, , tan x + cot x = .
The number of all possible values of , where 0< < , which the system of equations 
has a solution 
with 
, is
The number of all possible values of , where 0< < , which the system of equations has a solution with , is
Roots of the equation 
are
Roots of the equation are
The number of solutions of the pair of equations 
in the interval [0, 2] is
The number of solutions of the pair of equations in the interval [0, 2] is
can be made by 
in acidified medium. In which medium it can be estimated by 
?
then the value of 
