Advertisements
Advertisements
प्रश्न
Solve the following equation:
\[\cot x + \tan x = 2\]
Advertisements
उत्तर
\[ \Rightarrow \frac{1}{\tan x} + \tan x = 2\]
\[ \Rightarrow \tan^2 x + 1 = 2\tan x\]
\[ \Rightarrow \tan^2 x - 2\tan x + 1 = 0\]
\[ \Rightarrow \left( \tan x - 1 \right)^2 = 0\]
\[\Rightarrow \tan x = 1 = \tan\frac{\pi}{4}\]
\[ \Rightarrow x = n\pi + \frac{\pi}{4}, n \in Z \left( \tan\theta = \tan\alpha \Rightarrow \theta = n\pi + \alpha, n \in Z \right)\]
APPEARS IN
संबंधित प्रश्न
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
If tan θ + sec θ =ex, then cos θ equals
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:
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:
Solve the following equation:
Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
General solution of \[\tan 5 x = \cot 2 x\] is
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`
Solve the equation sin θ + sin 3θ + sin 5θ = 0
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 ______.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
