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
Find the general solution of cosec x = –2
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that:
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
In a ∆ABC, prove that:
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] 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 \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] 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
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:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
Solve the following equation:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Write the set of values of a for which the equation
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The smallest positive angle which satisfies the equation
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x
