Advertisements
Advertisements
प्रश्न
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
विकल्प
0
1
2
3
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 `tan x = sqrt3`
Find the general solution of the equation sin 2x + cos x = 0
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that
Prove that
Prove that:
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
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 A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
If tan θ + sec θ =ex, then cos θ equals
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
Solve the following equation:
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
