Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
उत्तर
We have:
\[\Rightarrow \cos x = - \sin 2x\]
\[ \Rightarrow \cos x = \cos \left( \frac{\pi}{2} + 2x \right)\]
\[ \Rightarrow x = 2n\pi \pm \left( \frac{\pi}{2} + 2x \right), n \in Z\]
On taking positive sign, we have:
\[x = 2n\pi + \frac{\pi}{2} + 2x\]
\[ \Rightarrow - x = 2n\pi + \frac{\pi}{2}\]
\[ \Rightarrow x = 2m\pi - \frac{\pi}{2}, m = - n \in Z\]
\[ \Rightarrow x = \frac{(4m - 1)\pi}{2}, m \in Z\]
On taking negative sign, we have:
`x-2nx-x/2-2x`
`=>3x=2nx-pi/2`
`=>x=((4n-1)x)/6,n in "Z"`
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the general solution of cosec x = –2
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 \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
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 tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
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
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
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:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]
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 tan x + sec x = 2 cos x in the interval [0, 2π].
Write the set of values of a for which the equation
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
