Advertisements
Advertisements
प्रश्न
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Advertisements
उत्तर
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
\[ \Rightarrow 5 \cos^2 x + 7\left( 1 - \cos^2 x \right) - 6 = 0\]
\[ \Rightarrow - 2 \cos^2 x + 1 = 0\]
\[ \Rightarrow \cos^2 x = \frac{1}{2} = \cos^2 \frac{\pi}{4}\]
\[ \Rightarrow x = n\pi \pm \frac{\pi}{4}, n \in Z \left( \cos^2 x = \cos^2 \alpha \Rightarrow x = n\pi \pm \alpha, n \in Z \right)\]
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the principal and general solutions of the equation `cot x = -sqrt3`
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
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
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:
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Write the set of values of a for which the equation
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 a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
If \[\cot x - \tan x = \sec x\], then, x is equal to
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of 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
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:
2cos 2x – 7 cos x + 3 = 0
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve the equation sin θ + sin 3θ + sin 5θ = 0
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
