Advertisements
Advertisements
प्रश्न
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
पर्याय
0
1
2
3
Advertisements
उत्तर
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is 3.
Explanation:
tanx + sec = 2cosx
sin + 1 = cos2x = sinx + 1= 2 - sin2x
2sin2x + sinx -1 = 0
(2sinx - 1) (sin + 1) = 0
but sinx = -1
`x= (3pi)/2`
`sinx = 1/2 = sin(pi/6)`
therefore the general solution is,
`x = npi + (-1)^n.pi/6`
`x = ...pi/6, (5pi)/6`
therefore, the number of solutions in the given interval is 3.
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that
Prove that
Prove that
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
Prove that:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
Prove that:
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
General solution of \[\tan 5 x = \cot 2 x\] is
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
