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 general solution of the equation cos 3x + cos x – cos 2x = 0
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 \[\tan x = \frac{a}{b},\] show that
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 \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
If tan θ + sec θ =ex, then cos θ equals
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
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:
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:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
3tanx + cot x = 5 cosec x
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the number of points of intersection of the curves
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
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:
sin θ + sin 3θ + sin 5θ = 0
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
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)`
