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 principal and general solutions of the equation sec x = 2
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Prove that:
Prove that
In a ∆ABC, prove that:
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:
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
If tan θ + sec θ =ex, then cos θ equals
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
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:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
3tanx + cot x = 5 cosec x
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
If \[\tan px - \tan qx = 0\], then the values of θ form a series in
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
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:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
