Advertisements
Advertisements
प्रश्न
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
उत्तर
\[4 \sin x \cos x + 2 \sin x + 2 \cos x + 1 = 0\]
\[ \Rightarrow 2 \sin x\left( 2 \cos x + 1 \right) + 1\left( 2 \cos x + 1 \right) = 0\]
\[ \Rightarrow \left( 2 \sin x + 1 \right)\left( 2 \cos x + 1 \right) = 0\]
\[ \Rightarrow 2 \sin x + 1 = 0\text{ or }2 \cos x + 1 = 0\]
\[ \Rightarrow \sin x = - \frac{1}{2} \text{ or }\cos x = - \frac{1}{2}\]
\[ \Rightarrow \sin x = \sin\frac{7\pi}{6}\text{ or }\cos x = \frac{2\pi}{3}\]
\[ \Rightarrow x = n\pi + \left( - 1 \right)^n \frac{7\pi}{6}\text{ or }x = 2n\pi \pm \frac{2\pi}{3}, n \in \mathbb{Z}\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation sin 2x + cos x = 0
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
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 \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 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:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
Prove that:
sin6 A + cos6 A + 3 sin2 A cos2 A =
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If tan θ + sec θ =ex, then cos θ equals
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
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:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
Solve the equation sin θ + sin 3θ + sin 5θ = 0
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
