>
Exams
>
Mathematics
>
Introduction to Trigonometry
>
if tan 3 1tan 3 1 3 then the general value of is
Question:
If
tan
3
θ
−
1
tan
3
θ
+
1
=
3
, then the general value of
θ
is:
JEE Main
Updated On:
Aug 2, 2023
n
π
3
−
π
12
,
n
∈
Z
n
π
+
7
π
12
,
n
∈
Z
n
π
3
+
7
π
36
,
n
∈
Z
n
π
+
π
12
,
n
∈
Z
Hide Solution
Verified By Collegedunia
The Correct Option is
C
Solution and Explanation
Explanation:
Given:
tan
3
θ
−
1
tan
3
θ
+
1
=
3
We have to find the general value of
θ
.
Consider,
tan
3
θ
−
1
tan
3
θ
+
1
=
3
⇒
tan
3
θ
−
tan
π
4
1
+
tan
3
θ
⋅
tan
π
4
=
3
[Using trigonometric ratios ]
⇒
tan
(
3
θ
−
π
4
)
=
tan
π
3
[Using trigonometric formula of tangent function ]
⇒
3
θ
−
π
4
=
n
π
+
π
3
,
n
∈
Z
[Using general solution of tangent function]
⇒
3
θ
=
n
π
+
π
3
+
π
4
,
n
∈
Z
⇒
3
θ
=
n
π
+
4
π
+
3
π
12
,
n
∈
Z
⇒
θ
=
n
π
3
+
7
π
36
,
n
∈
Z
Hence, the correct option is (C).
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Introduction to Trigonometry
If
\(sin(A-B)=\frac 12\)
and
\(cos(A+B)=\frac 12\)
, then
\(∠A, ∠B\)
?
TS POLYCET - 2022
Mathematics
Introduction to Trigonometry
View Solution
If
\(sin \ θ=cos\ θ\)
\((0<θ<90°)\)
, then
\(tan\ θ =\)
____ .
TS POLYCET - 2022
Mathematics
Introduction to Trigonometry
View Solution
If
\(tan(A-B)=\frac {1}{\sqrt 3},\ cos \ A=\frac 12 \)
then
\(∠B=\)
____ .
TS POLYCET - 2022
Mathematics
Introduction to Trigonometry
View Solution
The value of
\(\frac {tan\ α}{\sqrt {1+tan^2α}}\)
is ____ .
TS POLYCET - 2022
Mathematics
Introduction to Trigonometry
View Solution
In the right angle
\(△ABC,\ ∠B=90°\)
,
\(tan\ C=\frac {5}{12}\)
then the length of hypotenuse is
TS POLYCET - 2022
Mathematics
Introduction to Trigonometry
View Solution
View More Questions
Questions Asked in JEE Main exam
Let \( y = f(x) \) be the solution of the differential equation
\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\]
such that \( f(0) = 0 \). If
\[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\]
then \( \alpha^2 \) is equal to __________.
JEE Main - 2025
Differential equations
View Solution
Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is:
JEE Main - 2025
Statistics
View Solution
Let the system of equations
$ x + 5y - z = 1 $ $ 4x + 3y - 3z = 7 $ $ 24x + y + \lambda z = \mu $
where $ \lambda, \mu \in \mathbb{R} $, have infinitely many solutions. Then the number of the solutions of this system, if $x, y, z$ are integers and satisfy $7 \leq x + y + z \leq 77$, is:
JEE Main - 2025
Linear Systems and Determinants
View Solution
A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
JEE Main - 2025
Quantum Mechanics
View Solution
Match List-I with List-II:
List-I
JEE Main - 2025
Classification Of Organic Compounds
View Solution
View More Questions