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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
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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).
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