Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
उत्तर
We have:
\[\sin x = \frac{1}{2}\]
The value of x satisfying \[\sin x = \frac{1}{2}\] is \[\frac{\pi}{6}\]
⇒ \[x = n\pi + ( - 1 )^n \frac{\pi}{6}\]
APPEARS IN
संबंधित प्रश्न
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 the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
In a ∆ABC, prove that:
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
Prove that:
Prove that:
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
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 \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
If tan θ + sec θ =ex, then cos θ equals
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:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Write the number of points of intersection of the curves
Write the solution set of the equation
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then 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 the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
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 tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
