Advertisements
Advertisements
प्रश्न
Solve the following equation:
उत्तर
\[ \Rightarrow 4 \cos^2 x + 8 \cos x - 5 = 0\]
\[ \Rightarrow 4 \cos^2 x + 10 \cos x - 2 \cos x - 5 = 0\]
\[ \Rightarrow 2 \cos x (2 \cos x + 5 ) - 1 (2 \cos x + 5) = 0\]
\[ \Rightarrow (2 \cos x - 1) (2 \cos x + 5) = 0\]
\[\therefore 2 \cos x - 1 = 0 \]
\[ \Rightarrow \cos x = \frac{1}{2} \]
\[ \Rightarrow \cos x = \cos \frac{\pi}{3} \]
\[ \Rightarrow x = 2n\pi \pm \frac{\pi}{3}, n \in Z\]
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of the equation cos 4 x = cos 2 x
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
Prove that:
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
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
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
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
Which of the following is correct?
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:
Solve the following equation:
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
If \[\tan px - \tan qx = 0\], then the values of θ form a series in
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
General solution of \[\tan 5 x = \cot 2 x\] is
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
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
