Advertisements
Advertisements
प्रश्न
Solve the following equation:
उत्तर
\[ \Rightarrow \tan x (\tan x + 1) - \sqrt{3} (\tan x + 1) = 0\]
\[ \Rightarrow (\tan x - \sqrt{3}) (\tan x + 1) = 0\]
Now,
\[\tan x - \sqrt{3} = 0 \]
\[ \Rightarrow \tan x = \sqrt{3} \]
\[ \Rightarrow \tan x = \tan \frac{\pi}{3} \]
\[ \Rightarrow x = n\pi + \frac{\pi}{3}, n \in Z\]
And,
\[\tan x = - 1 \]
\[ \Rightarrow \tan x = \tan\left( - \frac{\pi}{4} \right) \]
\[ \Rightarrow x = m\pi - \frac{\pi}{4}, m \in Z\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
Find the general solution of the equation sin 2x + cos x = 0
Prove that:
Prove that:
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
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 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 =
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
Which of the following is incorrect?
Find the general solution of 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:
sin x tan x – 1 = tan x – sin x
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the solution set of the equation
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
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 number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The smallest positive angle which satisfies the equation
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
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°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
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`
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
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
