Advertisements
Advertisements
Question
Find the general solution of the following equation:
Advertisements
Solution
We have:
⇒ \[\sin9x - \sin x = 0\]
⇒ \[2 \sin \left( \frac{9x - x}{2} \right) \cos \left( \frac{9x + x}{2} \right) = 0\]
⇒ \[\sin \frac{8x}{2} = 0\] or \[\cos \frac{10x}{2} = 0\]
⇒ \[\sin 4x = 0\] or \[\cos 5x = 0\]
⇒ \[4x = n\pi\]
\[n \in Z\] or \[5x = (2n + 1)\frac{\pi}{2}\],
\[n \in Z\]
⇒ \[x = \frac{n\pi}{4}\],
\[n \in Z\] or \[x = (2n + 1)\frac{\pi}{10}\],
APPEARS IN
RELATED QUESTIONS
Find the general solution of the equation sin 2x + cos x = 0
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[\tan x = \frac{a}{b},\] show that
In a ∆ABC, prove that:
In a ∆ABC, prove that:
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
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 sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If tan θ + sec θ =ex, then cos θ equals
Which of the following is correct?
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:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
Write the number of points of intersection of the curves
Write the number of points of intersection of the curves
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
The smallest value of x satisfying the equation
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
General solution of \[\tan 5 x = \cot 2 x\] is
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:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
