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 general solution of cosec x = –2
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 \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
In a ∆ABC, prove that:
Prove that:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
Prove that:
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
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
If sec x + tan x = k, cos x =
Find the general solution of the following equation:
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
If \[4 \sin^2 x = 1\], then the values of x are
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
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:
tan θ = `- 1/sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
The minimum value of 3cosx + 4sinx + 8 is ______.
