>
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
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
If
\(A=45°,\ B=60°,\)
then
\(sin\ A+cos\ B\)
TS POLYCET - 2022
Mathematics
Introduction to Trigonometry
View Solution
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
View More Questions
Questions Asked in JEE Main exam
Let ABCD be a trapezium whose vertices lie on the parabola \( y^2 = 4x \). Let the sides AD and BC of the trapezium be parallel to the y-axis. If the diagonal AC is of length \( \frac{25}{4} \) and it passes through the point \( (1, 0) \), then the area of ABCD is:
JEE Main - 2025
Coordinate Geometry
View Solution
A molecule (P) on treatment with acid undergoes rearrangement and gives (Q). (Q) on ozonolysis followed by reflux under alkaline condition gives (R). The structure of (R) is given below. The structure of (P) is:
JEE Main - 2025
Organic Chemistry
View Solution
The product B formed in the following reaction sequence is:
\[ {C}_6{H}_5{CN} \xrightarrow{{HCl}} (A) \xrightarrow{{AgCN}} (B) \]
JEE Main - 2025
Organic Chemistry
View Solution
Let integers \( a, b \in [-3, 3] \) be such that \( a + b \neq 0 \).
\(\text{Then the number of all possible ordered pairs}\)
\( (a, b) \),
\(\text{for which}\)
\[ \left| \frac{z - a}{z + b} \right| = 1 \quad \text{and} \quad \left| \begin{matrix} z + 1 & \omega & \omega^2 \\ \omega^2 & 1 & z + \omega \\ \omega^2 & 1 & z + \omega \end{matrix} \right| = 1, \]
\(\text{is equal to:}\)
JEE Main - 2025
complex numbers
View Solution
Let \(E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1\) be an ellipse. Ellipses \(E_i\) are constructed such that their centers and eccentricities are the same as that of \(E_1\), and the length of the minor axis of \(E_{i+1}\) is the length of the major axis of \(E_i\). If \(A_i\) is the area of the ellipse \(E_i\), then \(\frac{5}{\pi} \sum_{i=1}^{\infty} A_i\) is equal to:
JEE Main - 2025
Calculus
View Solution
View More Questions