Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
Advertisements
उत्तर
We have:
\[\Rightarrow \tan mx = - \cot nx\]
\[ \Rightarrow \tan mx = \tan \left( \frac{\pi}{2} + nx \right)\]
\[ \Rightarrow mx = r\pi + \left( \frac{\pi}{2} + nx \right), r \in Z\]
\[ \Rightarrow (m - n) x = r\pi + \frac{\pi}{2}, r \in Z\]
\[ \Rightarrow x = \left( \frac{2r + 1}{m - n} \right)\frac{\pi}{2}, r \in Z\]
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of the equation sin 2x + cos x = 0
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 \[T_n = \sin^n x + \cos^n x\], 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:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
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:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
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 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
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
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:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]
Solve the following equation:
sin x tan x – 1 = tan x – sin x
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 values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
The smallest positive angle which satisfies the equation
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
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:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
