Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
Advertisements
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 `cot x = -sqrt3`
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that:
Prove that
In a ∆ABC, prove that:
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 \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\cot x + \tan x = 2\]
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
Write the set of values of a for which the equation
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
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 tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to
Solve the equation sin θ + sin 3θ + sin 5θ = 0
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
