Advertisements
Advertisements
प्रश्न
Solve the following equation:
उत्तर
\[\cos4x = \cos2x\]
\[ \Rightarrow 4x = 2n\pi \pm 2x , n \in Z\]
On taking positive sign, we have:
\[4x = 2n\pi + 2x\]
\[ \Rightarrow 2x = 2n\pi\]
\[ \Rightarrow x = n\pi, n \in Z\]
On taking negative sign, we have:
\[ \Rightarrow 6x = 2n\pi\]
\[ \Rightarrow x = \frac{n\pi}{3}, n \in Z\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation sin 2x + cos x = 0
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that:
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
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
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
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:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the set of values of a for which the equation
Write the number of points of intersection of the curves
Write the solution set of the equation
If \[\tan px - \tan qx = 0\], then the values of θ form a series in
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
Solve the equation sin θ + sin 3θ + sin 5θ = 0
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
The minimum value of 3cosx + 4sinx + 8 is ______.
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
