Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
Advertisements
उत्तर
We have:
\[\tan px = \cot qx\]
\[\Rightarrow \tan px = \tan \left( \frac{\pi}{2} - qx \right)\]
\[ \Rightarrow px = n\pi + \left( \frac{\pi}{2} - qx \right), n \in Z\]
\[ \Rightarrow (p + q)x = n\pi + \frac{\pi}{2}, n \in Z\]
\[ \Rightarrow x = \left( \frac{2n + 1}{p + q} \right)\frac{\pi}{2}, n \in Z\]
APPEARS IN
संबंधित प्रश्न
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 \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
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:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that
In a ∆ABC, prove that:
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 tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
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 \[f\left( x \right) = \cos^2 x + \sec^2 x\], 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:
`cosec x = 1 + cot x`
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the number of points of intersection of the curves
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
Write the number of points of intersection of the curves
Write the solution set of the equation
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
If \[\tan px - \tan qx = 0\], then the values of θ form a series in
If \[\cot x - \tan x = \sec x\], then, x is equal to
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Solve the equation sin θ + sin 3θ + sin 5θ = 0
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
