Advertisements
Advertisements
Question
Solve the following equation:
Advertisements
Solution
\[\sin 2x - \sin 4x + \sin 6x = 0\].
\[\Rightarrow 2 \sin \left( \frac{8x}{2} \right) \cos \left( \frac{4x}{2} \right) - \sin4x = 0\]
\[ \Rightarrow 2 \sin4x \cos2x - \sin4x = 0\]
\[ \Rightarrow \sin4x ( 2 \cos2x - 1) = 0\]
\[\Rightarrow 4x = n\pi\],
APPEARS IN
RELATED QUESTIONS
Find the principal and general solutions of the equation `tan x = sqrt3`
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] 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
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
Which of the following is incorrect?
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
Solve the following equation:
sin x tan x – 1 = tan x – sin x
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
Write the number of points of intersection of the curves
Write the number of points of intersection of the curves
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
If \[\cot x - \tan x = \sec x\], then, x is equal to
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
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.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
