>
Exams
>
Mathematics
>
integral
>
the number of solutions of the equation tan x sec
Question:
The number of solutions of the equation tan x + sec x = 2 cos x and cos x ≠ lying in the interval (0, 2π) is
WBJEE
Updated On:
Apr 27, 2024
(A) 2
(B) 1
(C) 0
(D) 3
Hide Solution
Verified By Collegedunia
The Correct Option is
D
Solution and Explanation
Explanation:
tan
x
+
sec
x
=
2
cos
x
1
+
sin
x
=
2
−
2
sin
2
x
2
sin
2
x
+
sin
x
−
1
=
0
(
2
sin
x
−
1
)
(
sin
x
+
1
)
=
0
sin
x
=
−
1
,
1
2
Therefore, number of solutions in
(
0
,
2
π
)
=
3
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on integral
Evaluate the integral:
$$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$
BITSAT - 2025
Mathematics
integral
View Solution
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
BITSAT - 2025
Mathematics
integral
View Solution
Evaluate the integral
\( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)
BITSAT - 2025
Mathematics
integral
View Solution
Evaluate the integral:
$$ \int_0^1 \frac{\ln (1+x)}{1+x^2} \, dx $$
AP EAPCET - 2025
Mathematics
integral
View Solution
Evaluate $ \int_{0}^{1} (3x^2 + 2x) \, dx $.
AP EAPCET - 2025
Mathematics
integral
View Solution
View More Questions
Questions Asked in WBJEE exam
Which logic gate is represented by the following combination of logic gates?
WBJEE - 2025
Logic gates
View Solution
If \( {}^9P_3 + 5 \cdot {}^9P_4 = {}^{10}P_r \), then the value of \( 'r' \) is:
WBJEE - 2025
permutations and combinations
View Solution
If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:
WBJEE - 2025
Trigonometric Equations
View Solution
Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to:
WBJEE - 2025
Matrix
View Solution
If \( a, b, c \) are in A.P. and if the equations \( (b - c)x^2 + (c - a)x + (a - b) = 0 \) and \( 2(c + a)x^2 + (b + c)x = 0 \) have a common root, then
WBJEE - 2025
Quadratic Equations
View Solution
View More Questions